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cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-menu mw-ui-icon-wikimedia-menu"></span> <span class="vector-dropdown-label-text">Галоўнае меню</span> </label> <div class="vector-dropdown-content"> <div id="vector-main-menu-unpinned-container" class="vector-unpinned-container"> <div id="vector-main-menu" class="vector-main-menu vector-pinnable-element"> <div class="vector-pinnable-header vector-main-menu-pinnable-header vector-pinnable-header-unpinned" data-feature-name="main-menu-pinned" data-pinnable-element-id="vector-main-menu" data-pinned-container-id="vector-main-menu-pinned-container" data-unpinned-container-id="vector-main-menu-unpinned-container" > <div class="vector-pinnable-header-label">Галоўнае меню</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-main-menu.pin">перанесці да бакавой панэлі</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-main-menu.unpin">схаваць</button> </div> <div id="p-navigation" class="vector-menu mw-portlet mw-portlet-navigation" > <div class="vector-menu-heading"> Навігацыя </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-mainpage" class="mw-list-item"><a href="/wiki/%D0%93%D0%B0%D0%BB%D0%BE%D1%9E%D0%BD%D0%B0%D1%8F_%D1%81%D1%82%D0%B0%D1%80%D0%BE%D0%BD%D0%BA%D0%B0" title="Адкрыць Галоўную старонку [z]" accesskey="z"><span>Галоўная старонка</span></a></li><li id="n-portal" class="mw-list-item"><a href="/wiki/%D0%92%D1%96%D0%BA%D1%96%D0%BF%D0%B5%D0%B4%D1%8B%D1%8F:%D0%A1%D1%83%D0%BF%D0%BE%D0%BB%D1%8C%D0%BD%D0%B0%D1%81%D1%86%D1%8C" title="Пра праект, чым можна заняцца, дзе што шукаць"><span>Супольнасць</span></a></li><li id="n-recentchanges" class="mw-list-item"><a href="/wiki/%D0%90%D0%B4%D0%BC%D1%8B%D1%81%D0%BB%D0%BE%D0%B2%D0%B0%D0%B5:RecentChanges" title="Пералік нядаўніх змяненняў у віксе. [r]" accesskey="r"><span>Апошнія змены</span></a></li><li id="n-newpages" class="mw-list-item"><a href="/wiki/%D0%90%D0%B4%D0%BC%D1%8B%D1%81%D0%BB%D0%BE%D0%B2%D0%B0%D0%B5:NewPages"><span>Новыя старонкі</span></a></li><li id="n-Village-pump" class="mw-list-item"><a href="/wiki/%D0%92%D1%96%D0%BA%D1%96%D0%BF%D0%B5%D0%B4%D1%8B%D1%8F:%D0%A4%D0%BE%D1%80%D1%83%D0%BC"><span>Форум</span></a></li><li id="n-randompage" class="mw-list-item"><a href="/wiki/%D0%90%D0%B4%D0%BC%D1%8B%D1%81%D0%BB%D0%BE%D0%B2%D0%B0%D0%B5:Random" title="Паказаць выпадковую старонку [x]" accesskey="x"><span>Выпадковая старонка</span></a></li><li id="n-help" class="mw-list-item"><a href="/wiki/%D0%92%D1%96%D0%BA%D1%96%D0%BF%D0%B5%D0%B4%D1%8B%D1%8F:%D0%94%D0%B0%D0%B2%D0%B5%D0%B4%D0%BA%D0%B0" title="Дзе можна атрымаць тлумачэнні."><span>Даведка</span></a></li><li id="n-bug_in_article" class="mw-list-item"><a href="/wiki/%D0%92%D1%96%D0%BA%D1%96%D0%BF%D0%B5%D0%B4%D1%8B%D1%8F:%D0%9F%D0%B0%D0%B2%D0%B5%D0%B4%D0%B0%D0%BC%D0%BB%D0%B5%D0%BD%D0%BD%D1%96_%D0%BF%D1%80%D0%B0_%D0%BF%D0%B0%D0%BC%D1%8B%D0%BB%D0%BA%D1%96"><span>Паведаміць пра памылку</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> <a href="/wiki/%D0%93%D0%B0%D0%BB%D0%BE%D1%9E%D0%BD%D0%B0%D1%8F_%D1%81%D1%82%D0%B0%D1%80%D0%BE%D0%BD%D0%BA%D0%B0" class="mw-logo"> <img class="mw-logo-icon" src="/static/images/icons/wikipedia.png" alt="" aria-hidden="true" height="50" width="50"> <span class="mw-logo-container skin-invert"> <img class="mw-logo-wordmark" alt="Вікіпедыя" src="/static/images/mobile/copyright/wikipedia-wordmark-be.svg" style="width: 7.625em; height: 1.3125em;"> <img class="mw-logo-tagline" alt="" src="/static/images/mobile/copyright/wikipedia-tagline-be.svg" width="117" height="12" style="width: 7.3125em; height: 0.75em;"> </span> </a> </div> <div class="vector-header-end"> <div id="p-search" role="search" class="vector-search-box-vue vector-search-box-collapses vector-search-box-show-thumbnail vector-search-box-auto-expand-width vector-search-box"> <a href="/wiki/%D0%90%D0%B4%D0%BC%D1%8B%D1%81%D0%BB%D0%BE%D0%B2%D0%B0%D0%B5:Search" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only search-toggle" title="Знайсці ў Вікіпедыі [f]" accesskey="f"><span class="vector-icon mw-ui-icon-search mw-ui-icon-wikimedia-search"></span> <span>Пошук</span> </a> <div class="vector-typeahead-search-container"> <div class="cdx-typeahead-search cdx-typeahead-search--show-thumbnail cdx-typeahead-search--auto-expand-width"> <form action="/w/index.php" id="searchform" class="cdx-search-input cdx-search-input--has-end-button"> <div id="simpleSearch" class="cdx-search-input__input-wrapper" data-search-loc="header-moved"> <div class="cdx-text-input cdx-text-input--has-start-icon"> <input class="cdx-text-input__input" type="search" name="search" placeholder="Шукаць у Вікіпедыі" aria-label="Шукаць у Вікіпедыі" autocapitalize="sentences" title="Знайсці ў Вікіпедыі [f]" accesskey="f" id="searchInput" > <span class="cdx-text-input__icon cdx-text-input__start-icon"></span> </div> <input type="hidden" name="title" value="Адмысловае:Search"> </div> <button class="cdx-button cdx-search-input__end-button">Пошук</button> </form> </div> </div> </div> <nav class="vector-user-links vector-user-links-wide" aria-label="Асабістыя інструменты"> <div class="vector-user-links-main"> <div id="p-vector-user-menu-preferences" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-userpage" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <nav class="vector-appearance-landmark" aria-label="Выгляд"> <div id="vector-appearance-dropdown" class="vector-dropdown " title="Change the appearance of the page's font size, width, and color" > <input type="checkbox" id="vector-appearance-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-appearance-dropdown" class="vector-dropdown-checkbox " aria-label="Выгляд" > <label id="vector-appearance-dropdown-label" for="vector-appearance-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-appearance mw-ui-icon-wikimedia-appearance"></span> <span class="vector-dropdown-label-text">Выгляд</span> </label> <div class="vector-dropdown-content"> <div id="vector-appearance-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <div id="p-vector-user-menu-notifications" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-overflow" class="vector-menu mw-portlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_be.wikipedia.org&uselang=be" class=""><span>Ахвяраваць</span></a> </li> <li id="pt-createaccount-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=%D0%90%D0%B4%D0%BC%D1%8B%D1%81%D0%BB%D0%BE%D0%B2%D0%B0%D0%B5:CreateAccount&returnto=%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0" title="Вам прапануецца стварыць уліковы запіс і ўвайсці ў сістэму, але гэта не абавязкова" class=""><span>Стварыць уліковы запіс</span></a> </li> <li id="pt-login-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=%D0%90%D0%B4%D0%BC%D1%8B%D1%81%D0%BB%D0%BE%D0%B2%D0%B0%D0%B5:UserLogin&returnto=%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0" title="Вам прапануецца ўвайсці ў сістэму, але гэта неабавязкова. [o]" accesskey="o" class=""><span>Увайсці</span></a> </li> </ul> </div> </div> </div> <div id="vector-user-links-dropdown" class="vector-dropdown vector-user-menu vector-button-flush-right vector-user-menu-logged-out" title="Больш магчымасцей" > <input type="checkbox" id="vector-user-links-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-user-links-dropdown" class="vector-dropdown-checkbox " aria-label="Асабістыя інструменты" > <label id="vector-user-links-dropdown-label" for="vector-user-links-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-ellipsis mw-ui-icon-wikimedia-ellipsis"></span> <span class="vector-dropdown-label-text">Асабістыя інструменты</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal user-links-collapsible-item" title="Меню ўдзельніка" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport" class="user-links-collapsible-item mw-list-item"><a href="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_be.wikipedia.org&uselang=be"><span>Ахвяраваць</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=%D0%90%D0%B4%D0%BC%D1%8B%D1%81%D0%BB%D0%BE%D0%B2%D0%B0%D0%B5:CreateAccount&returnto=%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0" title="Вам прапануецца стварыць уліковы запіс і ўвайсці ў сістэму, але гэта не абавязкова"><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>Стварыць уліковы запіс</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=%D0%90%D0%B4%D0%BC%D1%8B%D1%81%D0%BB%D0%BE%D0%B2%D0%B0%D0%B5:UserLogin&returnto=%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0" title="Вам прапануецца ўвайсці ў сістэму, але гэта неабавязкова. [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>Увайсці</span></a></li> </ul> </div> </div> <div id="p-user-menu-anon-editor" class="vector-menu mw-portlet mw-portlet-user-menu-anon-editor" > <div class="vector-menu-heading"> Старонкі для ананімных рэдактараў <a href="/wiki/%D0%94%D0%B0%D0%B2%D0%B5%D0%B4%D0%BA%D0%B0:%D0%94%D0%B0%D0%B2%D0%B5%D0%B4%D0%BA%D0%B0" aria-label="Даведацца больш пра праўку"><span>даведацца больш</span></a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/%D0%90%D0%B4%D0%BC%D1%8B%D1%81%D0%BB%D0%BE%D0%B2%D0%B0%D0%B5:MyContributions" title="Спіс правак, зробленых з гэтага IP-адраса [y]" accesskey="y"><span>Уклад</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/%D0%90%D0%B4%D0%BC%D1%8B%D1%81%D0%BB%D0%BE%D0%B2%D0%B0%D0%B5:MyTalk" title="Размовы пра праўкі, зробленыя з гэтага IP-адраса [n]" accesskey="n"><span>Размовы</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> </header> </div> <div class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="Праект"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="Змест" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">Змест</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">перанесці да бакавой панэлі</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">схаваць</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">Пачатак</div> </a> </li> <li id="toc-Этымалогія_назвы" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Этымалогія_назвы"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Этымалогія назвы</span> </div> </a> <ul id="toc-Этымалогія_назвы-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Гісторыя" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Гісторыя"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Гісторыя</span> </div> </a> <button aria-controls="toc-Гісторыя-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Змяніць стан падраздзелу Гісторыя</span> </button> <ul id="toc-Гісторыя-sublist" class="vector-toc-list"> <li id="toc-Старажытны_свет" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Старажытны_свет"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Старажытны свет</span> </div> </a> <ul id="toc-Старажытны_свет-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Развіццё_сімволікі" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Развіццё_сімволікі"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Развіццё сімволікі</span> </div> </a> <ul id="toc-Развіццё_сімволікі-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Далейшыя_поспехі" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Далейшыя_поспехі"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3</span> <span>Далейшыя поспехі</span> </div> </a> <ul id="toc-Далейшыя_поспехі-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Лінейная_алгебра" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Лінейная_алгебра"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Лінейная алгебра</span> </div> </a> <ul id="toc-Лінейная_алгебра-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Агульная_алгебра" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Агульная_алгебра"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Агульная алгебра</span> </div> </a> <button aria-controls="toc-Агульная_алгебра-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Змяніць стан падраздзелу Агульная алгебра</span> </button> <ul id="toc-Агульная_алгебра-sublist" class="vector-toc-list"> <li id="toc-Тэорыя_груп" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Тэорыя_груп"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>Тэорыя груп</span> </div> </a> <ul id="toc-Тэорыя_груп-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Тэорыя_кольцаў" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Тэорыя_кольцаў"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2</span> <span>Тэорыя кольцаў</span> </div> </a> <ul id="toc-Тэорыя_кольцаў-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Універсальная_алгебра" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Універсальная_алгебра"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Універсальная алгебра</span> </div> </a> <ul id="toc-Універсальная_алгебра-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Крыніцы" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Крыніцы"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Крыніцы</span> </div> </a> <ul id="toc-Крыніцы-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Спасылкі" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Спасылкі"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Спасылкі</span> </div> </a> <ul id="toc-Спасылкі-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Змест" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Пераключыць змест" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Пераключыць змест</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Алгебра</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Перайсці да артыкула на іншай мове. Даступны на 167 мовах." > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-167" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">167 моў</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Algebra" title="Algebra – афрыкаанс" lang="af" hreflang="af" data-title="Algebra" data-language-autonym="Afrikaans" data-language-local-name="афрыкаанс" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-als mw-list-item"><a href="https://als.wikipedia.org/wiki/Algebra" title="Algebra – швейцарская нямецкая" lang="gsw" hreflang="gsw" data-title="Algebra" data-language-autonym="Alemannisch" data-language-local-name="швейцарская нямецкая" class="interlanguage-link-target"><span>Alemannisch</span></a></li><li class="interlanguage-link interwiki-am mw-list-item"><a href="https://am.wikipedia.org/wiki/%E1%8A%A0%E1%88%8D%E1%8C%80%E1%89%A5%E1%88%AB" title="አልጀብራ – амхарская" lang="am" hreflang="am" data-title="አልጀብራ" data-language-autonym="አማርኛ" data-language-local-name="амхарская" class="interlanguage-link-target"><span>አማርኛ</span></a></li><li class="interlanguage-link interwiki-an mw-list-item"><a href="https://an.wikipedia.org/wiki/Alchebra" title="Alchebra – арагонская" lang="an" hreflang="an" data-title="Alchebra" data-language-autonym="Aragonés" data-language-local-name="арагонская" class="interlanguage-link-target"><span>Aragonés</span></a></li><li class="interlanguage-link interwiki-ang mw-list-item"><a href="https://ang.wikipedia.org/wiki/R%C4%ABmagiefung" title="Rīmagiefung – стараанглійская" lang="ang" hreflang="ang" data-title="Rīmagiefung" data-language-autonym="Ænglisc" data-language-local-name="стараанглійская" class="interlanguage-link-target"><span>Ænglisc</span></a></li><li class="interlanguage-link interwiki-anp mw-list-item"><a href="https://anp.wikipedia.org/wiki/%E0%A4%AC%E0%A5%80%E0%A4%9C%E0%A4%97%E0%A4%A3%E0%A4%BF%E0%A4%A4" title="बीजगणित – ангіка" lang="anp" hreflang="anp" data-title="बीजगणित" data-language-autonym="अंगिका" data-language-local-name="ангіка" class="interlanguage-link-target"><span>अंगिका</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%A7%D9%84%D8%AC%D8%A8%D8%B1" title="الجبر – арабская" lang="ar" hreflang="ar" data-title="الجبر" data-language-autonym="العربية" data-language-local-name="арабская" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-arz mw-list-item"><a href="https://arz.wikipedia.org/wiki/%D8%AC%D8%A8%D8%B1" title="جبر – Egyptian Arabic" lang="arz" hreflang="arz" data-title="جبر" data-language-autonym="مصرى" data-language-local-name="Egyptian Arabic" class="interlanguage-link-target"><span>مصرى</span></a></li><li class="interlanguage-link interwiki-as mw-list-item"><a href="https://as.wikipedia.org/wiki/%E0%A6%AC%E0%A7%80%E0%A6%9C%E0%A6%97%E0%A6%A3%E0%A6%BF%E0%A6%A4" title="বীজগণিত – асамская" lang="as" hreflang="as" data-title="বীজগণিত" data-language-autonym="অসমীয়া" data-language-local-name="асамская" class="interlanguage-link-target"><span>অসমীয়া</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/%C3%81lxebra" title="Álxebra – астурыйская" lang="ast" hreflang="ast" data-title="Álxebra" data-language-autonym="Asturianu" data-language-local-name="астурыйская" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/C%C9%99br" title="Cəbr – азербайджанская" lang="az" hreflang="az" data-title="Cəbr" data-language-autonym="Azərbaycanca" data-language-local-name="азербайджанская" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-azb mw-list-item"><a href="https://azb.wikipedia.org/wiki/%D8%AC%D8%A8%D8%B1" title="جبر – South Azerbaijani" lang="azb" hreflang="azb" data-title="جبر" data-language-autonym="تۆرکجه" data-language-local-name="South Azerbaijani" class="interlanguage-link-target"><span>تۆرکجه</span></a></li><li class="interlanguage-link interwiki-ba mw-list-item"><a href="https://ba.wikipedia.org/wiki/%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0" title="Алгебра – башкірская" lang="ba" hreflang="ba" data-title="Алгебра" data-language-autonym="Башҡортса" data-language-local-name="башкірская" class="interlanguage-link-target"><span>Башҡортса</span></a></li><li class="interlanguage-link interwiki-bat-smg mw-list-item"><a href="https://bat-smg.wikipedia.org/wiki/Algebra" title="Algebra – Samogitian" lang="sgs" hreflang="sgs" data-title="Algebra" data-language-autonym="Žemaitėška" data-language-local-name="Samogitian" class="interlanguage-link-target"><span>Žemaitėška</span></a></li><li class="interlanguage-link interwiki-bcl mw-list-item"><a href="https://bcl.wikipedia.org/wiki/Alhebra" title="Alhebra – Central Bikol" lang="bcl" hreflang="bcl" data-title="Alhebra" data-language-autonym="Bikol Central" data-language-local-name="Central Bikol" class="interlanguage-link-target"><span>Bikol Central</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%90%D0%BB%D1%8C%D0%B3%D0%B5%D0%B1%D1%80%D0%B0" title="Альгебра – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Альгебра" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0" title="Алгебра – балгарская" lang="bg" hreflang="bg" data-title="Алгебра" data-language-autonym="Български" data-language-local-name="балгарская" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bh mw-list-item"><a href="https://bh.wikipedia.org/wiki/%E0%A4%AC%E0%A5%80%E0%A4%9C%E0%A4%97%E0%A4%A3%E0%A4%BF%E0%A4%A4" title="बीजगणित – Bhojpuri" lang="bh" hreflang="bh" data-title="बीजगणित" data-language-autonym="भोजपुरी" data-language-local-name="Bhojpuri" class="interlanguage-link-target"><span>भोजपुरी</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%AC%E0%A7%80%E0%A6%9C%E0%A6%97%E0%A6%A3%E0%A6%BF%E0%A6%A4" title="বীজগণিত – бенгальская" lang="bn" hreflang="bn" data-title="বীজগণিত" data-language-autonym="বাংলা" data-language-local-name="бенгальская" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-bo mw-list-item"><a href="https://bo.wikipedia.org/wiki/%E0%BD%9A%E0%BD%96%E0%BC%8B%E0%BD%A2%E0%BE%A9%E0%BD%B2%E0%BD%A6%E0%BC%8D" title="ཚབ་རྩིས། – тыбецкая" lang="bo" hreflang="bo" data-title="ཚབ་རྩིས།" data-language-autonym="བོད་ཡིག" data-language-local-name="тыбецкая" class="interlanguage-link-target"><span>བོད་ཡིག</span></a></li><li class="interlanguage-link interwiki-br mw-list-item"><a href="https://br.wikipedia.org/wiki/Aljebr" title="Aljebr – брэтонская" lang="br" hreflang="br" data-title="Aljebr" data-language-autonym="Brezhoneg" data-language-local-name="брэтонская" class="interlanguage-link-target"><span>Brezhoneg</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Algebra" title="Algebra – баснійская" lang="bs" hreflang="bs" data-title="Algebra" data-language-autonym="Bosanski" data-language-local-name="баснійская" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/%C3%80lgebra" title="Àlgebra – каталанская" lang="ca" hreflang="ca" data-title="Àlgebra" data-language-autonym="Català" data-language-local-name="каталанская" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cdo mw-list-item"><a href="https://cdo.wikipedia.org/wiki/D%C3%A2i-s%C3%B3" title="Dâi-só – Mindong" lang="cdo" hreflang="cdo" data-title="Dâi-só" data-language-autonym="閩東語 / Mìng-dĕ̤ng-ngṳ̄" data-language-local-name="Mindong" class="interlanguage-link-target"><span>閩東語 / Mìng-dĕ̤ng-ngṳ̄</span></a></li><li class="interlanguage-link interwiki-ce mw-list-item"><a href="https://ce.wikipedia.org/wiki/%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0" title="Алгебра – чачэнская" lang="ce" hreflang="ce" data-title="Алгебра" data-language-autonym="Нохчийн" data-language-local-name="чачэнская" class="interlanguage-link-target"><span>Нохчийн</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D8%AC%DB%95%D8%A8%D8%B1" title="جەبر – цэнтральнакурдская" lang="ckb" hreflang="ckb" data-title="جەبر" data-language-autonym="کوردی" data-language-local-name="цэнтральнакурдская" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-co mw-list-item"><a href="https://co.wikipedia.org/wiki/Algebra" title="Algebra – карсіканская" lang="co" hreflang="co" data-title="Algebra" data-language-autonym="Corsu" data-language-local-name="карсіканская" class="interlanguage-link-target"><span>Corsu</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Algebra" title="Algebra – чэшская" lang="cs" hreflang="cs" data-title="Algebra" data-language-autonym="Čeština" data-language-local-name="чэшская" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0" title="Алгебра – чувашская" lang="cv" hreflang="cv" data-title="Алгебра" data-language-autonym="Чӑвашла" data-language-local-name="чувашская" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Algebra" title="Algebra – валійская" lang="cy" hreflang="cy" data-title="Algebra" data-language-autonym="Cymraeg" data-language-local-name="валійская" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Algebra" title="Algebra – дацкая" lang="da" hreflang="da" data-title="Algebra" data-language-autonym="Dansk" data-language-local-name="дацкая" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Algebra" title="Algebra – нямецкая" lang="de" hreflang="de" data-title="Algebra" data-language-autonym="Deutsch" data-language-local-name="нямецкая" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-diq mw-list-item"><a href="https://diq.wikipedia.org/wiki/Cebir" title="Cebir – Zazaki" lang="diq" hreflang="diq" data-title="Cebir" data-language-autonym="Zazaki" data-language-local-name="Zazaki" class="interlanguage-link-target"><span>Zazaki</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%86%CE%BB%CE%B3%CE%B5%CE%B2%CF%81%CE%B1" title="Άλγεβρα – грэчаская" lang="el" hreflang="el" data-title="Άλγεβρα" data-language-autonym="Ελληνικά" data-language-local-name="грэчаская" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-eml mw-list-item"><a href="https://eml.wikipedia.org/wiki/Algebra" title="Algebra – Emiliano-Romagnolo" lang="egl" hreflang="egl" data-title="Algebra" data-language-autonym="Emiliàn e rumagnòl" data-language-local-name="Emiliano-Romagnolo" class="interlanguage-link-target"><span>Emiliàn e rumagnòl</span></a></li><li class="interlanguage-link interwiki-en badge-Q17437796 badge-featuredarticle mw-list-item" title="выдатны артыкул"><a href="https://en.wikipedia.org/wiki/Algebra" title="Algebra – англійская" lang="en" hreflang="en" data-title="Algebra" data-language-autonym="English" data-language-local-name="англійская" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Algebro" title="Algebro – эсперанта" lang="eo" hreflang="eo" data-title="Algebro" data-language-autonym="Esperanto" data-language-local-name="эсперанта" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/%C3%81lgebra" title="Álgebra – іспанская" lang="es" hreflang="es" data-title="Álgebra" data-language-autonym="Español" data-language-local-name="іспанская" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Algebra" title="Algebra – эстонская" lang="et" hreflang="et" data-title="Algebra" data-language-autonym="Eesti" data-language-local-name="эстонская" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Aljebra" title="Aljebra – баскская" lang="eu" hreflang="eu" data-title="Aljebra" data-language-autonym="Euskara" data-language-local-name="баскская" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%AC%D8%A8%D8%B1" title="جبر – фарсі" lang="fa" hreflang="fa" data-title="جبر" data-language-autonym="فارسی" data-language-local-name="фарсі" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Algebra" title="Algebra – фінская" lang="fi" hreflang="fi" data-title="Algebra" data-language-autonym="Suomi" data-language-local-name="фінская" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fiu-vro mw-list-item"><a href="https://fiu-vro.wikipedia.org/wiki/Alg%C3%B5bra" title="Algõbra – Võro" lang="vro" hreflang="vro" data-title="Algõbra" data-language-autonym="Võro" data-language-local-name="Võro" class="interlanguage-link-target"><span>Võro</span></a></li><li class="interlanguage-link interwiki-fj mw-list-item"><a href="https://fj.wikipedia.org/wiki/Ivakavakadina" title="Ivakavakadina – фіджыйская" lang="fj" hreflang="fj" data-title="Ivakavakadina" data-language-autonym="Na Vosa Vakaviti" data-language-local-name="фіджыйская" class="interlanguage-link-target"><span>Na Vosa Vakaviti</span></a></li><li class="interlanguage-link interwiki-fo mw-list-item"><a href="https://fo.wikipedia.org/wiki/Algebra" title="Algebra – фарэрская" lang="fo" hreflang="fo" data-title="Algebra" data-language-autonym="Føroyskt" data-language-local-name="фарэрская" class="interlanguage-link-target"><span>Føroyskt</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Alg%C3%A8bre" title="Algèbre – французская" lang="fr" hreflang="fr" data-title="Algèbre" data-language-autonym="Français" data-language-local-name="французская" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-frr mw-list-item"><a href="https://frr.wikipedia.org/wiki/Algebra" title="Algebra – паўночнафрызская" lang="frr" hreflang="frr" data-title="Algebra" data-language-autonym="Nordfriisk" data-language-local-name="паўночнафрызская" class="interlanguage-link-target"><span>Nordfriisk</span></a></li><li class="interlanguage-link interwiki-fy mw-list-item"><a href="https://fy.wikipedia.org/wiki/Algebra" title="Algebra – заходняя фрызская" lang="fy" hreflang="fy" data-title="Algebra" data-language-autonym="Frysk" data-language-local-name="заходняя фрызская" class="interlanguage-link-target"><span>Frysk</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Ailg%C3%A9abar" title="Ailgéabar – ірландская" lang="ga" hreflang="ga" data-title="Ailgéabar" data-language-autonym="Gaeilge" data-language-local-name="ірландская" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gan mw-list-item"><a href="https://gan.wikipedia.org/wiki/%E4%BB%A3%E6%95%B8" title="代數 – Gan" lang="gan" hreflang="gan" data-title="代數" data-language-autonym="贛語" data-language-local-name="Gan" class="interlanguage-link-target"><span>贛語</span></a></li><li class="interlanguage-link interwiki-gcr mw-list-item"><a href="https://gcr.wikipedia.org/wiki/Aj%C3%A8b" title="Ajèb – Guianan Creole" lang="gcr" hreflang="gcr" data-title="Ajèb" data-language-autonym="Kriyòl gwiyannen" data-language-local-name="Guianan Creole" class="interlanguage-link-target"><span>Kriyòl gwiyannen</span></a></li><li class="interlanguage-link interwiki-gd mw-list-item"><a href="https://gd.wikipedia.org/wiki/Ailseabra" title="Ailseabra – шатландская гэльская" lang="gd" hreflang="gd" data-title="Ailseabra" data-language-autonym="Gàidhlig" data-language-local-name="шатландская гэльская" class="interlanguage-link-target"><span>Gàidhlig</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/%C3%81lxebra" title="Álxebra – галісійская" lang="gl" hreflang="gl" data-title="Álxebra" data-language-autonym="Galego" data-language-local-name="галісійская" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-gn mw-list-item"><a href="https://gn.wikipedia.org/wiki/%C3%81lgebra" title="Álgebra – гуарані" lang="gn" hreflang="gn" data-title="Álgebra" data-language-autonym="Avañe'ẽ" data-language-local-name="гуарані" class="interlanguage-link-target"><span>Avañe'ẽ</span></a></li><li class="interlanguage-link interwiki-gu mw-list-item"><a href="https://gu.wikipedia.org/wiki/%E0%AA%AC%E0%AB%80%E0%AA%9C%E0%AA%97%E0%AA%A3%E0%AA%BF%E0%AA%A4" title="બીજગણિત – гуджараці" lang="gu" hreflang="gu" data-title="બીજગણિત" data-language-autonym="ગુજરાતી" data-language-local-name="гуджараці" class="interlanguage-link-target"><span>ગુજરાતી</span></a></li><li class="interlanguage-link interwiki-gv mw-list-item"><a href="https://gv.wikipedia.org/wiki/Algeerey" title="Algeerey – мэнская" lang="gv" hreflang="gv" data-title="Algeerey" data-language-autonym="Gaelg" data-language-local-name="мэнская" class="interlanguage-link-target"><span>Gaelg</span></a></li><li class="interlanguage-link interwiki-ha mw-list-item"><a href="https://ha.wikipedia.org/wiki/Algebra" title="Algebra – хауса" lang="ha" hreflang="ha" data-title="Algebra" data-language-autonym="Hausa" data-language-local-name="хауса" class="interlanguage-link-target"><span>Hausa</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%90%D7%9C%D7%92%D7%91%D7%A8%D7%94" title="אלגברה – іўрыт" lang="he" hreflang="he" data-title="אלגברה" data-language-autonym="עברית" data-language-local-name="іўрыт" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%AC%E0%A5%80%E0%A4%9C%E0%A4%97%E0%A4%A3%E0%A4%BF%E0%A4%A4" title="बीजगणित – хіндзі" lang="hi" hreflang="hi" data-title="बीजगणित" data-language-autonym="हिन्दी" data-language-local-name="хіндзі" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hif mw-list-item"><a href="https://hif.wikipedia.org/wiki/Algebra" title="Algebra – Fiji Hindi" lang="hif" hreflang="hif" data-title="Algebra" data-language-autonym="Fiji Hindi" data-language-local-name="Fiji Hindi" class="interlanguage-link-target"><span>Fiji Hindi</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Algebra" title="Algebra – харвацкая" lang="hr" hreflang="hr" data-title="Algebra" data-language-autonym="Hrvatski" data-language-local-name="харвацкая" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Alj%C3%A8b" title="Aljèb – гаіцянская крэольская" lang="ht" hreflang="ht" data-title="Aljèb" data-language-autonym="Kreyòl ayisyen" data-language-local-name="гаіцянская крэольская" class="interlanguage-link-target"><span>Kreyòl ayisyen</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Algebra" title="Algebra – венгерская" lang="hu" hreflang="hu" data-title="Algebra" data-language-autonym="Magyar" data-language-local-name="венгерская" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%80%D5%A1%D5%B6%D6%80%D5%A1%D5%B0%D5%A1%D5%B7%D5%AB%D5%BE" title="Հանրահաշիվ – армянская" lang="hy" hreflang="hy" data-title="Հանրահաշիվ" data-language-autonym="Հայերեն" data-language-local-name="армянская" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Algebra" title="Algebra – інтэрлінгва" lang="ia" hreflang="ia" data-title="Algebra" data-language-autonym="Interlingua" data-language-local-name="інтэрлінгва" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-iba mw-list-item"><a href="https://iba.wikipedia.org/wiki/Algebra" title="Algebra – ібан" lang="iba" hreflang="iba" data-title="Algebra" data-language-autonym="Jaku Iban" data-language-local-name="ібан" class="interlanguage-link-target"><span>Jaku Iban</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Aljabar" title="Aljabar – інданезійская" lang="id" hreflang="id" data-title="Aljabar" data-language-autonym="Bahasa Indonesia" data-language-local-name="інданезійская" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-ilo mw-list-item"><a href="https://ilo.wikipedia.org/wiki/Alhebra" title="Alhebra – ілакана" lang="ilo" hreflang="ilo" data-title="Alhebra" data-language-autonym="Ilokano" data-language-local-name="ілакана" class="interlanguage-link-target"><span>Ilokano</span></a></li><li class="interlanguage-link interwiki-inh mw-list-item"><a href="https://inh.wikipedia.org/wiki/%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0" title="Алгебра – інгушская" lang="inh" hreflang="inh" data-title="Алгебра" data-language-autonym="ГӀалгӀай" data-language-local-name="інгушская" class="interlanguage-link-target"><span>ГӀалгӀай</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Algebro" title="Algebro – іда" lang="io" hreflang="io" data-title="Algebro" data-language-autonym="Ido" data-language-local-name="іда" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Algebra" title="Algebra – ісландская" lang="is" hreflang="is" data-title="Algebra" data-language-autonym="Íslenska" data-language-local-name="ісландская" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Algebra" title="Algebra – італьянская" lang="it" hreflang="it" data-title="Algebra" data-language-autonym="Italiano" data-language-local-name="італьянская" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E4%BB%A3%E6%95%B0%E5%AD%A6" title="代数学 – японская" lang="ja" hreflang="ja" data-title="代数学" data-language-autonym="日本語" data-language-local-name="японская" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-jam mw-list-item"><a href="https://jam.wikipedia.org/wiki/Aljibra" title="Aljibra – Jamaican Creole English" lang="jam" hreflang="jam" data-title="Aljibra" data-language-autonym="Patois" data-language-local-name="Jamaican Creole English" class="interlanguage-link-target"><span>Patois</span></a></li><li class="interlanguage-link interwiki-jbo mw-list-item"><a href="https://jbo.wikipedia.org/wiki/alxebra" title="alxebra – ложбан" lang="jbo" hreflang="jbo" data-title="alxebra" data-language-autonym="La .lojban." data-language-local-name="ложбан" class="interlanguage-link-target"><span>La .lojban.</span></a></li><li class="interlanguage-link interwiki-jv mw-list-item"><a href="https://jv.wikipedia.org/wiki/Aljabar" title="Aljabar – яванская" lang="jv" hreflang="jv" data-title="Aljabar" data-language-autonym="Jawa" data-language-local-name="яванская" class="interlanguage-link-target"><span>Jawa</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%90%E1%83%9A%E1%83%92%E1%83%94%E1%83%91%E1%83%A0%E1%83%90" title="ალგებრა – грузінская" lang="ka" hreflang="ka" data-title="ალგებრა" data-language-autonym="ქართული" data-language-local-name="грузінская" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kaa mw-list-item"><a href="https://kaa.wikipedia.org/wiki/Algebra" title="Algebra – Kara-Kalpak" lang="kaa" hreflang="kaa" data-title="Algebra" data-language-autonym="Qaraqalpaqsha" data-language-local-name="Kara-Kalpak" class="interlanguage-link-target"><span>Qaraqalpaqsha</span></a></li><li class="interlanguage-link interwiki-kab mw-list-item"><a href="https://kab.wikipedia.org/wiki/Aljiber" title="Aljiber – кабільская" lang="kab" hreflang="kab" data-title="Aljiber" data-language-autonym="Taqbaylit" data-language-local-name="кабільская" class="interlanguage-link-target"><span>Taqbaylit</span></a></li><li class="interlanguage-link interwiki-kbd mw-list-item"><a href="https://kbd.wikipedia.org/wiki/%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D1%8D" title="Алгебрэ – кабардзінская" lang="kbd" hreflang="kbd" data-title="Алгебрэ" data-language-autonym="Адыгэбзэ" data-language-local-name="кабардзінская" class="interlanguage-link-target"><span>Адыгэбзэ</span></a></li><li class="interlanguage-link interwiki-kbp mw-list-item"><a href="https://kbp.wikipedia.org/wiki/%C3%91%CA%8A%C5%8B_kal%CA%8A%CA%8A_t%CA%8Am%C9%A9y%C9%9B" title="Ñʊŋ kalʊʊ tʊmɩyɛ – Kabiye" lang="kbp" hreflang="kbp" data-title="Ñʊŋ kalʊʊ tʊmɩyɛ" data-language-autonym="Kabɩyɛ" data-language-local-name="Kabiye" class="interlanguage-link-target"><span>Kabɩyɛ</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0" title="Алгебра – казахская" lang="kk" hreflang="kk" data-title="Алгебра" data-language-autonym="Қазақша" data-language-local-name="казахская" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%AC%E0%B3%80%E0%B2%9C%E0%B2%97%E0%B2%A3%E0%B2%BF%E0%B2%A4" title="ಬೀಜಗಣಿತ – канада" lang="kn" hreflang="kn" data-title="ಬೀಜಗಣಿತ" data-language-autonym="ಕನ್ನಡ" data-language-local-name="канада" class="interlanguage-link-target"><span>ಕನ್ನಡ</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%8C%80%EC%88%98%ED%95%99" title="대수학 – карэйская" lang="ko" hreflang="ko" data-title="대수학" data-language-autonym="한국어" data-language-local-name="карэйская" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-kw mw-list-item"><a href="https://kw.wikipedia.org/wiki/Aljebra" title="Aljebra – корнская" lang="kw" hreflang="kw" data-title="Aljebra" data-language-autonym="Kernowek" data-language-local-name="корнская" class="interlanguage-link-target"><span>Kernowek</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0" title="Алгебра – кіргізская" lang="ky" hreflang="ky" data-title="Алгебра" data-language-autonym="Кыргызча" data-language-local-name="кіргізская" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Algebra" title="Algebra – лацінская" lang="la" hreflang="la" data-title="Algebra" data-language-autonym="Latina" data-language-local-name="лацінская" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lfn mw-list-item"><a href="https://lfn.wikipedia.org/wiki/Aljebra" title="Aljebra – Lingua Franca Nova" lang="lfn" hreflang="lfn" data-title="Aljebra" data-language-autonym="Lingua Franca Nova" data-language-local-name="Lingua Franca Nova" class="interlanguage-link-target"><span>Lingua Franca Nova</span></a></li><li class="interlanguage-link interwiki-lg mw-list-item"><a href="https://lg.wikipedia.org/wiki/Aligebbula" title="Aligebbula – ганда" lang="lg" hreflang="lg" data-title="Aligebbula" data-language-autonym="Luganda" data-language-local-name="ганда" class="interlanguage-link-target"><span>Luganda</span></a></li><li class="interlanguage-link interwiki-li mw-list-item"><a href="https://li.wikipedia.org/wiki/Algebra" title="Algebra – лімбургская" lang="li" hreflang="li" data-title="Algebra" data-language-autonym="Limburgs" data-language-local-name="лімбургская" class="interlanguage-link-target"><span>Limburgs</span></a></li><li class="interlanguage-link interwiki-lij mw-list-item"><a href="https://lij.wikipedia.org/wiki/Algebra" title="Algebra – Ligurian" lang="lij" hreflang="lij" data-title="Algebra" data-language-autonym="Ligure" data-language-local-name="Ligurian" class="interlanguage-link-target"><span>Ligure</span></a></li><li class="interlanguage-link interwiki-lmo mw-list-item"><a href="https://lmo.wikipedia.org/wiki/Algebra" title="Algebra – Lombard" lang="lmo" hreflang="lmo" data-title="Algebra" data-language-autonym="Lombard" data-language-local-name="Lombard" class="interlanguage-link-target"><span>Lombard</span></a></li><li class="interlanguage-link interwiki-lo mw-list-item"><a href="https://lo.wikipedia.org/wiki/%E0%BA%9E%E0%BA%B6%E0%BA%94%E0%BA%8A%E0%BA%B0%E0%BA%84%E0%BA%B0%E0%BA%99%E0%BA%B4%E0%BA%94" title="ພຶດຊະຄະນິດ – лаоская" lang="lo" hreflang="lo" data-title="ພຶດຊະຄະນິດ" data-language-autonym="ລາວ" data-language-local-name="лаоская" class="interlanguage-link-target"><span>ລາວ</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Algebra" title="Algebra – літоўская" lang="lt" hreflang="lt" data-title="Algebra" data-language-autonym="Lietuvių" data-language-local-name="літоўская" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Algebra" title="Algebra – латышская" lang="lv" hreflang="lv" data-title="Algebra" data-language-autonym="Latviešu" data-language-local-name="латышская" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-mg mw-list-item"><a href="https://mg.wikipedia.org/wiki/Aljebra" title="Aljebra – малагасійская" lang="mg" hreflang="mg" data-title="Aljebra" data-language-autonym="Malagasy" data-language-local-name="малагасійская" class="interlanguage-link-target"><span>Malagasy</span></a></li><li class="interlanguage-link interwiki-min mw-list-item"><a href="https://min.wikipedia.org/wiki/Aljabar" title="Aljabar – мінангкабау" lang="min" hreflang="min" data-title="Aljabar" data-language-autonym="Minangkabau" data-language-local-name="мінангкабау" class="interlanguage-link-target"><span>Minangkabau</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0" title="Алгебра – македонская" lang="mk" hreflang="mk" data-title="Алгебра" data-language-autonym="Македонски" data-language-local-name="македонская" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%AC%E0%B5%80%E0%B4%9C%E0%B4%97%E0%B4%A3%E0%B4%BF%E0%B4%A4%E0%B4%82" title="ബീജഗണിതം – малаялам" lang="ml" hreflang="ml" data-title="ബീജഗണിതം" data-language-autonym="മലയാളം" data-language-local-name="малаялам" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%AC%E0%A5%80%E0%A4%9C%E0%A4%97%E0%A4%A3%E0%A4%BF%E0%A4%A4" title="बीजगणित – маратхі" lang="mr" hreflang="mr" data-title="बीजगणित" data-language-autonym="मराठी" data-language-local-name="маратхі" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Algebra" title="Algebra – малайская" lang="ms" hreflang="ms" data-title="Algebra" data-language-autonym="Bahasa Melayu" data-language-local-name="малайская" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-mt mw-list-item"><a href="https://mt.wikipedia.org/wiki/Al%C4%A1ebra" title="Alġebra – мальтыйская" lang="mt" hreflang="mt" data-title="Alġebra" data-language-autonym="Malti" data-language-local-name="мальтыйская" class="interlanguage-link-target"><span>Malti</span></a></li><li class="interlanguage-link interwiki-mwl mw-list-item"><a href="https://mwl.wikipedia.org/wiki/%C3%81lgebra" title="Álgebra – мірандыйская" lang="mwl" hreflang="mwl" data-title="Álgebra" data-language-autonym="Mirandés" data-language-local-name="мірандыйская" class="interlanguage-link-target"><span>Mirandés</span></a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%A1%E1%80%80%E1%80%B9%E1%80%81%E1%80%9B%E1%80%AC%E1%80%9E%E1%80%84%E1%80%BA%E1%80%B9%E1%80%81%E1%80%BB%E1%80%AC" title="အက္ခရာသင်္ချာ – бірманская" lang="my" hreflang="my" data-title="အက္ခရာသင်္ချာ" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="бірманская" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-nds mw-list-item"><a href="https://nds.wikipedia.org/wiki/Algebra" title="Algebra – ніжненямецкая" lang="nds" hreflang="nds" data-title="Algebra" data-language-autonym="Plattdüütsch" data-language-local-name="ніжненямецкая" class="interlanguage-link-target"><span>Plattdüütsch</span></a></li><li class="interlanguage-link interwiki-ne mw-list-item"><a href="https://ne.wikipedia.org/wiki/%E0%A4%AC%E0%A4%BF%E0%A4%9C%E0%A4%97%E0%A4%A3%E0%A4%BF%E0%A4%A4" title="बिजगणित – непальская" lang="ne" hreflang="ne" data-title="बिजगणित" data-language-autonym="नेपाली" data-language-local-name="непальская" class="interlanguage-link-target"><span>नेपाली</span></a></li><li class="interlanguage-link interwiki-new mw-list-item"><a href="https://new.wikipedia.org/wiki/%E0%A4%AC%E0%A5%80%E0%A4%9C%E0%A4%97%E0%A4%A3%E0%A4%BF%E0%A4%A4" title="बीजगणित – неўары" lang="new" hreflang="new" data-title="बीजगणित" data-language-autonym="नेपाल भाषा" data-language-local-name="неўары" class="interlanguage-link-target"><span>नेपाल भाषा</span></a></li><li class="interlanguage-link interwiki-nia mw-list-item"><a href="https://nia.wikipedia.org/wiki/Aljabar" title="Aljabar – ніас" lang="nia" hreflang="nia" data-title="Aljabar" data-language-autonym="Li Niha" data-language-local-name="ніас" class="interlanguage-link-target"><span>Li Niha</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Algebra" title="Algebra – нідэрландская" lang="nl" hreflang="nl" data-title="Algebra" data-language-autonym="Nederlands" data-language-local-name="нідэрландская" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Algebra" title="Algebra – нарвежская (нюношк)" lang="nn" hreflang="nn" data-title="Algebra" data-language-autonym="Norsk nynorsk" data-language-local-name="нарвежская (нюношк)" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Algebra" title="Algebra – нарвежская (букмол)" lang="nb" hreflang="nb" data-title="Algebra" data-language-autonym="Norsk bokmål" data-language-local-name="нарвежская (букмол)" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-nov mw-list-item"><a href="https://nov.wikipedia.org/wiki/Algebra" title="Algebra – Novial" lang="nov" hreflang="nov" data-title="Algebra" data-language-autonym="Novial" data-language-local-name="Novial" class="interlanguage-link-target"><span>Novial</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Alg%C3%A8bra" title="Algèbra – аксітанская" lang="oc" hreflang="oc" data-title="Algèbra" data-language-autonym="Occitan" data-language-local-name="аксітанская" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-om mw-list-item"><a href="https://om.wikipedia.org/wiki/Aljebraa" title="Aljebraa – арома" lang="om" hreflang="om" data-title="Aljebraa" data-language-autonym="Oromoo" data-language-local-name="арома" class="interlanguage-link-target"><span>Oromoo</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%85%E0%A8%B2%E0%A8%9C%E0%A8%AC%E0%A8%B0%E0%A8%BE" title="ਅਲਜਬਰਾ – панджабі" lang="pa" hreflang="pa" data-title="ਅਲਜਬਰਾ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="панджабі" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Algebra" title="Algebra – польская" lang="pl" hreflang="pl" data-title="Algebra" data-language-autonym="Polski" data-language-local-name="польская" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/%C3%80lgebra" title="Àlgebra – Piedmontese" lang="pms" hreflang="pms" data-title="Àlgebra" data-language-autonym="Piemontèis" data-language-local-name="Piedmontese" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%D8%A7%D9%84%D8%AC%D8%A8%D8%B1%D8%A7" title="الجبرا – Western Punjabi" lang="pnb" hreflang="pnb" data-title="الجبرا" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target"><span>پنجابی</span></a></li><li class="interlanguage-link interwiki-ps mw-list-item"><a href="https://ps.wikipedia.org/wiki/%D8%A7%D9%84%D8%AC%D8%A8%D8%B1" title="الجبر – пушту" lang="ps" hreflang="ps" data-title="الجبر" data-language-autonym="پښتو" data-language-local-name="пушту" class="interlanguage-link-target"><span>پښتو</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/%C3%81lgebra" title="Álgebra – партугальская" lang="pt" hreflang="pt" data-title="Álgebra" data-language-autonym="Português" data-language-local-name="партугальская" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-qu mw-list-item"><a href="https://qu.wikipedia.org/wiki/Qillqanancha_kamay" title="Qillqanancha kamay – кечуа" lang="qu" hreflang="qu" data-title="Qillqanancha kamay" data-language-autonym="Runa Simi" data-language-local-name="кечуа" class="interlanguage-link-target"><span>Runa Simi</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Algebr%C4%83" title="Algebră – румынская" lang="ro" hreflang="ro" data-title="Algebră" data-language-autonym="Română" data-language-local-name="румынская" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0" title="Алгебра – руская" lang="ru" hreflang="ru" data-title="Алгебра" data-language-autonym="Русский" data-language-local-name="руская" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-rue mw-list-item"><a href="https://rue.wikipedia.org/wiki/%D0%90%D0%BB%D2%91%D0%B5%D0%B1%D1%80%D0%B0" title="Алґебра – Rusyn" lang="rue" hreflang="rue" data-title="Алґебра" data-language-autonym="Русиньскый" data-language-local-name="Rusyn" class="interlanguage-link-target"><span>Русиньскый</span></a></li><li class="interlanguage-link interwiki-sah mw-list-item"><a href="https://sah.wikipedia.org/wiki/%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0" title="Алгебра – якуцкая" lang="sah" hreflang="sah" data-title="Алгебра" data-language-autonym="Саха тыла" data-language-local-name="якуцкая" class="interlanguage-link-target"><span>Саха тыла</span></a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/%C3%80lgibbra" title="Àlgibbra – сіцылійская" lang="scn" hreflang="scn" data-title="Àlgibbra" data-language-autonym="Sicilianu" data-language-local-name="сіцылійская" class="interlanguage-link-target"><span>Sicilianu</span></a></li><li class="interlanguage-link interwiki-sco mw-list-item"><a href="https://sco.wikipedia.org/wiki/Algebra" title="Algebra – шатландская" lang="sco" hreflang="sco" data-title="Algebra" data-language-autonym="Scots" data-language-local-name="шатландская" class="interlanguage-link-target"><span>Scots</span></a></li><li class="interlanguage-link interwiki-sd mw-list-item"><a href="https://sd.wikipedia.org/wiki/%D8%A2%D9%84%D8%AC%D8%A8%D8%B1%D8%A7" title="آلجبرا – сіндхі" lang="sd" hreflang="sd" data-title="آلجبرا" data-language-autonym="سنڌي" data-language-local-name="сіндхі" class="interlanguage-link-target"><span>سنڌي</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Algebra" title="Algebra – сербскахарвацкая" lang="sh" hreflang="sh" data-title="Algebra" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="сербскахарвацкая" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-shi mw-list-item"><a href="https://shi.wikipedia.org/wiki/Aljibr" title="Aljibr – ташэльхіт" lang="shi" hreflang="shi" data-title="Aljibr" data-language-autonym="Taclḥit" data-language-local-name="ташэльхіт" class="interlanguage-link-target"><span>Taclḥit</span></a></li><li class="interlanguage-link interwiki-si mw-list-item"><a href="https://si.wikipedia.org/wiki/%E0%B7%80%E0%B7%93%E0%B6%A2_%E0%B6%9C%E0%B6%AB%E0%B7%92%E0%B6%AD%E0%B6%BA" title="වීජ ගණිතය – сінгальская" lang="si" hreflang="si" data-title="වීජ ගණිතය" data-language-autonym="සිංහල" data-language-local-name="сінгальская" class="interlanguage-link-target"><span>සිංහල</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Algebra" title="Algebra – Simple English" lang="en-simple" hreflang="en-simple" data-title="Algebra" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Algebra_(discipl%C3%ADna)" title="Algebra (disciplína) – славацкая" lang="sk" hreflang="sk" data-title="Algebra (disciplína)" data-language-autonym="Slovenčina" data-language-local-name="славацкая" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Algebra" title="Algebra – славенская" lang="sl" hreflang="sl" data-title="Algebra" data-language-autonym="Slovenščina" data-language-local-name="славенская" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-so mw-list-item"><a href="https://so.wikipedia.org/wiki/Aljebra" title="Aljebra – самалі" lang="so" hreflang="so" data-title="Aljebra" data-language-autonym="Soomaaliga" data-language-local-name="самалі" class="interlanguage-link-target"><span>Soomaaliga</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Algjebra" title="Algjebra – албанская" lang="sq" hreflang="sq" data-title="Algjebra" data-language-autonym="Shqip" data-language-local-name="албанская" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0" title="Алгебра – сербская" lang="sr" hreflang="sr" data-title="Алгебра" data-language-autonym="Српски / srpski" data-language-local-name="сербская" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-su mw-list-item"><a href="https://su.wikipedia.org/wiki/Aljabar" title="Aljabar – сунда" lang="su" hreflang="su" data-title="Aljabar" data-language-autonym="Sunda" data-language-local-name="сунда" class="interlanguage-link-target"><span>Sunda</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Algebra" title="Algebra – шведская" lang="sv" hreflang="sv" data-title="Algebra" data-language-autonym="Svenska" data-language-local-name="шведская" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-sw mw-list-item"><a href="https://sw.wikipedia.org/wiki/Aljebra" title="Aljebra – суахілі" lang="sw" hreflang="sw" data-title="Aljebra" data-language-autonym="Kiswahili" data-language-local-name="суахілі" class="interlanguage-link-target"><span>Kiswahili</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%87%E0%AE%AF%E0%AE%B1%E0%AF%8D%E0%AE%95%E0%AE%A3%E0%AE%BF%E0%AE%A4%E0%AE%AE%E0%AF%8D" title="இயற்கணிதம் – тамільская" lang="ta" hreflang="ta" data-title="இயற்கணிதம்" data-language-autonym="தமிழ்" data-language-local-name="тамільская" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-te mw-list-item"><a href="https://te.wikipedia.org/wiki/%E0%B0%AC%E0%B1%80%E0%B0%9C_%E0%B0%97%E0%B0%A3%E0%B0%BF%E0%B0%A4%E0%B0%82" title="బీజ గణితం – тэлугу" lang="te" hreflang="te" data-title="బీజ గణితం" data-language-autonym="తెలుగు" data-language-local-name="тэлугу" class="interlanguage-link-target"><span>తెలుగు</span></a></li><li class="interlanguage-link interwiki-tg mw-list-item"><a href="https://tg.wikipedia.org/wiki/%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0" title="Алгебра – таджыкская" lang="tg" hreflang="tg" data-title="Алгебра" data-language-autonym="Тоҷикӣ" data-language-local-name="таджыкская" class="interlanguage-link-target"><span>Тоҷикӣ</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%9E%E0%B8%B5%E0%B8%8A%E0%B8%84%E0%B8%93%E0%B8%B4%E0%B8%95" title="พีชคณิต – тайская" lang="th" hreflang="th" data-title="พีชคณิต" data-language-autonym="ไทย" data-language-local-name="тайская" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tk mw-list-item"><a href="https://tk.wikipedia.org/wiki/Algebra" title="Algebra – туркменская" lang="tk" hreflang="tk" data-title="Algebra" data-language-autonym="Türkmençe" data-language-local-name="туркменская" class="interlanguage-link-target"><span>Türkmençe</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Alhebra" title="Alhebra – Tagalog" lang="tl" hreflang="tl" data-title="Alhebra" data-language-autonym="Tagalog" data-language-local-name="Tagalog" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Cebir" title="Cebir – турэцкая" lang="tr" hreflang="tr" data-title="Cebir" data-language-autonym="Türkçe" data-language-local-name="турэцкая" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-ts mw-list-item"><a href="https://ts.wikipedia.org/wiki/Tinhlayo-swiyenge" title="Tinhlayo-swiyenge – тсонга" lang="ts" hreflang="ts" data-title="Tinhlayo-swiyenge" data-language-autonym="Xitsonga" data-language-local-name="тсонга" class="interlanguage-link-target"><span>Xitsonga</span></a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0" title="Алгебра – татарская" lang="tt" hreflang="tt" data-title="Алгебра" data-language-autonym="Татарча / tatarça" data-language-local-name="татарская" class="interlanguage-link-target"><span>Татарча / tatarça</span></a></li><li class="interlanguage-link interwiki-tum mw-list-item"><a href="https://tum.wikipedia.org/wiki/Alijebra" title="Alijebra – тумбука" lang="tum" hreflang="tum" data-title="Alijebra" data-language-autonym="ChiTumbuka" data-language-local-name="тумбука" class="interlanguage-link-target"><span>ChiTumbuka</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0" title="Алгебра – украінская" lang="uk" hreflang="uk" data-title="Алгебра" data-language-autonym="Українська" data-language-local-name="украінская" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D8%A7%D9%84%D8%AC%D8%A8%D8%B1%D8%A7" title="الجبرا – урду" lang="ur" hreflang="ur" data-title="الجبرا" data-language-autonym="اردو" data-language-local-name="урду" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Algebra" title="Algebra – узбекская" lang="uz" hreflang="uz" data-title="Algebra" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="узбекская" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-vec mw-list-item"><a href="https://vec.wikipedia.org/wiki/%C3%80lgebra" title="Àlgebra – Venetian" lang="vec" hreflang="vec" data-title="Àlgebra" data-language-autonym="Vèneto" data-language-local-name="Venetian" class="interlanguage-link-target"><span>Vèneto</span></a></li><li class="interlanguage-link interwiki-vep mw-list-item"><a href="https://vep.wikipedia.org/wiki/Algebr" title="Algebr – Veps" lang="vep" hreflang="vep" data-title="Algebr" data-language-autonym="Vepsän kel’" data-language-local-name="Veps" class="interlanguage-link-target"><span>Vepsän kel’</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/%C4%90%E1%BA%A1i_s%E1%BB%91" title="Đại số – в’етнамская" lang="vi" hreflang="vi" data-title="Đại số" data-language-autonym="Tiếng Việt" data-language-local-name="в’етнамская" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-vls mw-list-item"><a href="https://vls.wikipedia.org/wiki/Algebra" title="Algebra – West Flemish" lang="vls" hreflang="vls" data-title="Algebra" data-language-autonym="West-Vlams" data-language-local-name="West Flemish" class="interlanguage-link-target"><span>West-Vlams</span></a></li><li class="interlanguage-link interwiki-war mw-list-item"><a href="https://war.wikipedia.org/wiki/Alhebra" title="Alhebra – варай" lang="war" hreflang="war" data-title="Alhebra" data-language-autonym="Winaray" data-language-local-name="варай" class="interlanguage-link-target"><span>Winaray</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E4%BB%A3%E6%95%B0" title="代数 – ву" lang="wuu" hreflang="wuu" data-title="代数" data-language-autonym="吴语" data-language-local-name="ву" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-xh mw-list-item"><a href="https://xh.wikipedia.org/wiki/I-Algebra" title="I-Algebra – коса" lang="xh" hreflang="xh" data-title="I-Algebra" data-language-autonym="IsiXhosa" data-language-local-name="коса" class="interlanguage-link-target"><span>IsiXhosa</span></a></li><li class="interlanguage-link interwiki-xmf mw-list-item"><a href="https://xmf.wikipedia.org/wiki/%E1%83%90%E1%83%9A%E1%83%92%E1%83%94%E1%83%91%E1%83%A0%E1%83%90" title="ალგებრა – Mingrelian" lang="xmf" hreflang="xmf" data-title="ალგებრა" data-language-autonym="მარგალური" data-language-local-name="Mingrelian" class="interlanguage-link-target"><span>მარგალური</span></a></li><li class="interlanguage-link interwiki-yi mw-list-item"><a href="https://yi.wikipedia.org/wiki/%D7%90%D7%9C%D7%92%D7%A2%D7%91%D7%A8%D7%A2" title="אלגעברע – ідыш" lang="yi" hreflang="yi" data-title="אלגעברע" data-language-autonym="ייִדיש" data-language-local-name="ідыш" class="interlanguage-link-target"><span>ייִדיש</span></a></li><li class="interlanguage-link interwiki-yo mw-list-item"><a href="https://yo.wikipedia.org/wiki/Algebra" title="Algebra – ёруба" lang="yo" hreflang="yo" data-title="Algebra" data-language-autonym="Yorùbá" data-language-local-name="ёруба" class="interlanguage-link-target"><span>Yorùbá</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E4%BB%A3%E6%95%B0" title="代数 – кітайская" lang="zh" hreflang="zh" data-title="代数" data-language-autonym="中文" data-language-local-name="кітайская" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-classical mw-list-item"><a href="https://zh-classical.wikipedia.org/wiki/%E4%BB%A3%E6%95%B8%E5%AD%B8" title="代數學 – Literary Chinese" lang="lzh" hreflang="lzh" data-title="代數學" data-language-autonym="文言" data-language-local-name="Literary Chinese" class="interlanguage-link-target"><span>文言</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/T%C4%81i-s%C3%B2%CD%98" title="Tāi-sò͘ – Minnan" lang="nan" hreflang="nan" data-title="Tāi-sò͘" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="Minnan" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E4%BB%A3%E6%95%B8%E5%AD%B8" title="代數學 – кантонскі дыялект кітайскай" lang="yue" hreflang="yue" data-title="代數學" 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href="/wiki/%D0%A4%D0%B0%D0%B9%D0%BB:Right_concoid.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/af/Right_concoid.svg/180px-Right_concoid.svg.png" decoding="async" width="180" height="193" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/af/Right_concoid.svg/270px-Right_concoid.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/af/Right_concoid.svg/360px-Right_concoid.svg.png 2x" data-file-width="560" data-file-height="600" /></a><figcaption>Трохмерны правабаковы кананоід, апісаны элементарнымі алгебраічнымі ўраўненнямі<center><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x=v\times \cos(u),}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mo>=</mo> <mi>v</mi> <mo>×</mo> <mi>cos</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>u</mi> <mo stretchy="false">)</mo> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x=v\times \cos(u),}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/71a00483ef2c845c1b6116c4b2efaeb605384e8b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:15.293ex; height:2.843ex;" alt="{\displaystyle x=v\times \cos(u),}"></span> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle y=v\times \sin(u),}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>y</mi> <mo>=</mo> <mi>v</mi> <mo>×</mo> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>u</mi> <mo stretchy="false">)</mo> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y=v\times \sin(u),}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7ff64dcbf300ebf55bcadabedee275a4a9f88449" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:14.863ex; height:2.843ex;" alt="{\displaystyle y=v\times \sin(u),}"></span> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle z=2\times \sin(u).}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>z</mi> <mo>=</mo> <mn>2</mn> <mo>×</mo> <mi>sin</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>u</mi> <mo stretchy="false">)</mo> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle z=2\times \sin(u).}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a2e6f4513761a3e527c77a265a8a1cb52ca1970b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:14.831ex; height:2.843ex;" alt="{\displaystyle z=2\times \sin(u).}"></span></center></figcaption></figure> <p><b>А́лгебра</b> (<a href="/wiki/%D0%90%D1%80%D0%B0%D0%B1%D1%81%D0%BA%D0%B0%D1%8F_%D0%BC%D0%BE%D0%B2%D0%B0" title="Арабская мова">араб.</a> <span lang="ar" style="font-size: 130%">الجبر</span>‎‎ «аль-джабр» — уз’яднанне, дапаўненне) — адзін з найстарэйшых раздзелаў <a href="/wiki/%D0%9C%D0%B0%D1%82%D1%8D%D0%BC%D0%B0%D1%82%D1%8B%D0%BA%D0%B0" title="Матэматыка">матэматыкі</a>, які ўзнік яшчэ ў старажытнасці. Алгебра вывучае алгебраічныя структуры, аперацыі над элементамі <a href="/wiki/%D0%9C%D0%BD%D0%BE%D1%81%D1%82%D0%B2%D0%B0" title="Мноства">мностваў</a>, аперацыі <a href="/wiki/%D0%A1%D0%BA%D0%BB%D0%B0%D0%B4%D0%B0%D0%BD%D0%BD%D0%B5" title="Складанне">складання</a> і <a href="/wiki/%D0%9C%D0%BD%D0%BE%D0%B6%D0%B0%D0%BD%D0%BD%D0%B5" title="Множанне">множання</a>, паняцці <a href="/wiki/%D0%97%D0%BC%D0%B5%D0%BD%D0%BD%D0%B0%D1%8F_%D0%B2%D0%B5%D0%BB%D1%96%D1%87%D1%8B%D0%BD%D1%8F" title="Зменная велічыня">зменных</a> і г. д. Вывучэнне ўласцівасцей кампазіцый рознага віду ў <a href="/wiki/19_%D1%81%D1%82%D0%B0%D0%B3%D0%BE%D0%B4%D0%B4%D0%B7%D0%B5" class="mw-redirect" title="19 стагоддзе">XIX стагоддзі</a> прывяло да думкі, што асноўнай задачай алгебры з’яўляецца вывучэнне ўласцівасцей аперацый незалежна ад аб’ектаў, да якіх яны прымяняюцца. З тых часоў алгебра пачала разглядацца як агульная навука аб уласцівасцях і законах кампазіцыі аперацый. У нашы дні алгебра — адна з найважнейшых частак матэматыкі, якая знаходзіць прымяненне як у тэарэтычных, так і ў практычных галінах навукі. </p><p>Сярод асноўных паняццяў, з якімі мае справу алгебра: </p> <ul><li><a href="/wiki/%D0%97%D0%BC%D0%B5%D0%BD%D0%BD%D0%B0%D1%8F_%D0%B2%D0%B5%D0%BB%D1%96%D1%87%D1%8B%D0%BD%D1%8F" title="Зменная велічыня">зменная велічыня</a></li> <li><a href="/wiki/%D0%A0%D0%BE%D1%9E%D0%BD%D0%B0%D1%81%D1%86%D1%8C" title="Роўнасць">роўнасць</a></li> <li><a href="/wiki/%D0%9D%D1%8F%D1%80%D0%BE%D1%9E%D0%BD%D0%B0%D1%81%D1%86%D1%8C" title="Няроўнасць">няроўнасць</a></li> <li><a href="/wiki/%D0%A3%D1%80%D0%B0%D1%9E%D0%BD%D0%B5%D0%BD%D0%BD%D0%B5" title="Ураўненне">ураўненне</a></li> <li><a href="/wiki/%D0%9C%D0%BD%D0%B0%D0%B3%D0%B0%D1%87%D0%BB%D0%B5%D0%BD" title="Мнагачлен">мнагачлен</a></li></ul> <p>Больш шырока алгебру разумеюць як навуку аб якасных і колькасных адносінах, якія ўзнікаюць у розных структурах (не абавязкова лікавых) — напрыклад, <a href="/wiki/%D0%9F%D0%BE%D0%BB%D0%B5_(%D0%B0%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0)" title="Поле (алгебра)">палях</a>, <a href="/wiki/%D0%93%D1%80%D1%83%D0%BF%D0%B0_(%D0%B0%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0)" title="Група (алгебра)">групах</a>, <a href="/wiki/%D0%9A%D0%B0%D0%BB%D1%8C%D1%86%D0%BE_(%D0%B0%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0)" title="Кальцо (алгебра)">колцах</a>. </p><p>У адпаведнасці з гэтым разглядаюць такія раздзелы алгебры: </p> <ul><li><a href="/wiki/%D0%AD%D0%BB%D0%B5%D0%BC%D0%B5%D0%BD%D1%82%D0%B0%D1%80%D0%BD%D0%B0%D1%8F_%D0%B0%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0" title="Элементарная алгебра">элементарная алгебра</a> — галіна алгебры, якая вывучае <a href="/wiki/%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0%D1%96%D1%87%D0%BD%D1%8B_%D0%B2%D1%8B%D1%80%D0%B0%D0%B7" title="Алгебраічны выраз">алгебраічныя выразы</a> над лікамі;</li> <li><a href="/wiki/%D0%90%D0%B1%D1%81%D1%82%D1%80%D0%B0%D0%BA%D1%82%D0%BD%D0%B0%D1%8F_%D0%B0%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0" title="Абстрактная алгебра">абстрактная алгебра</a> — галіна алгебры, якая вывучае <a href="/w/index.php?title=%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0%D1%96%D1%87%D0%BD%D0%B0%D1%8F_%D1%81%D1%82%D1%80%D1%83%D0%BA%D1%82%D1%83%D1%80%D0%B0&action=edit&redlink=1" class="new" title="Алгебраічная структура (няма такой старонкі)">алгебраічныя структуры</a>, вызначаныя <a href="/w/index.php?title=%D0%90%D0%BA%D1%81%D1%96%D1%8F%D0%BC%D0%B0%D1%82%D1%8B%D0%BA%D0%B0&action=edit&redlink=1" class="new" title="Аксіяматыка (няма такой старонкі)">аксіяматычна</a>.</li></ul> <p>Алгебра з’яўляецца адной з асноўных галін <a href="/wiki/%D0%9C%D0%B0%D1%82%D1%8D%D0%BC%D0%B0%D1%82%D1%8B%D0%BA%D0%B0" title="Матэматыка">матэматыкі</a> разам з <a href="/wiki/%D0%93%D0%B5%D0%B0%D0%BC%D0%B5%D1%82%D1%80%D1%8B%D1%8F" title="Геаметрыя">геаметрыяй</a>, <a href="/wiki/%D0%9C%D0%B0%D1%82%D1%8D%D0%BC%D0%B0%D1%82%D1%8B%D1%87%D0%BD%D1%8B_%D0%B0%D0%BD%D0%B0%D0%BB%D1%96%D0%B7" title="Матэматычны аналіз">аналізам</a>, <a href="/wiki/%D0%A2%D0%B0%D0%BF%D0%B0%D0%BB%D0%BE%D0%B3%D1%96%D1%8F" title="Тапалогія">тапалогіяй</a>, <a href="/wiki/%D0%9A%D0%B0%D0%BC%D0%B1%D1%96%D0%BD%D0%B0%D1%82%D0%BE%D1%80%D1%8B%D0%BA%D0%B0" title="Камбінаторыка">камбінаторыкай</a> і <a href="/wiki/%D0%A2%D1%8D%D0%BE%D1%80%D1%8B%D1%8F_%D0%BB%D1%96%D0%BA%D0%B0%D1%9E" title="Тэорыя лікаў">тэорыяй лікаў</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Этымалогія_назвы"><span id=".D0.AD.D1.82.D1.8B.D0.BC.D0.B0.D0.BB.D0.BE.D0.B3.D1.96.D1.8F_.D0.BD.D0.B0.D0.B7.D0.B2.D1.8B"></span>Этымалогія назвы</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0&veaction=edit&section=1" title="Правіць раздзел: Этымалогія назвы" class="mw-editsection-visualeditor"><span>правіць</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0&action=edit&section=1" title="Правіць зыходнік раздзела: Этымалогія назвы"><span>правіць зыходнік</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Найменне «алгебра» ўжываецца ў розных алгебраічных сістэмах. Слова «алгебра» паходзіць ад назвы адной з першых кніг па алгебры «<i>Hisab al-dżabr wa’l-mukabala</i>» (<i>Кніга вылічэнняў шляхам дапаўнення і раўнавагі</i>), якую ў <a href="/wiki/825" title="825">825</a> годзе напісаў арабскі навуковец <a href="/wiki/%D0%90%D0%BB%D1%8C-%D0%A5%D0%B0%D1%80%D1%8D%D0%B7%D0%BC%D1%96" class="mw-redirect" title="Аль-Харэзмі">Аль-Харэзмі</a>. Даслоўна яно азначае «<i>папаўненне</i>». </p> <div class="mw-heading mw-heading2"><h2 id="Гісторыя"><span id=".D0.93.D1.96.D1.81.D1.82.D0.BE.D1.80.D1.8B.D1.8F"></span>Гісторыя</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0&veaction=edit&section=2" title="Правіць раздзел: Гісторыя" class="mw-editsection-visualeditor"><span>правіць</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0&action=edit&section=2" title="Правіць зыходнік раздзела: Гісторыя"><span>правіць зыходнік</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Старажытны_свет"><span id=".D0.A1.D1.82.D0.B0.D1.80.D0.B0.D0.B6.D1.8B.D1.82.D0.BD.D1.8B_.D1.81.D0.B2.D0.B5.D1.82"></span>Старажытны свет</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0&veaction=edit&section=3" title="Правіць раздзел: Старажытны свет" class="mw-editsection-visualeditor"><span>правіць</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0&action=edit&section=3" title="Правіць зыходнік раздзела: Старажытны свет"><span>правіць зыходнік</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/%D0%A4%D0%B0%D0%B9%D0%BB:Sanzio_01_Euclid.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/81/Sanzio_01_Euclid.jpg/180px-Sanzio_01_Euclid.jpg" decoding="async" width="180" height="212" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/81/Sanzio_01_Euclid.jpg/270px-Sanzio_01_Euclid.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/81/Sanzio_01_Euclid.jpg/360px-Sanzio_01_Euclid.jpg 2x" data-file-width="930" data-file-height="1094" /></a><figcaption>Старажытнагрэчаскі матэматык <a href="/wiki/%D0%AD%D1%9E%D0%BA%D0%BB%D1%96%D0%B4" title="Эўклід">Эўклід</a> (ці <a href="/wiki/%D0%90%D1%80%D1%85%D1%96%D0%BC%D0%B5%D0%B4" title="Архімед">Архімед</a>) з вучнямі. Фрэска «<a href="/wiki/%D0%90%D1%84%D1%96%D0%BD%D1%81%D0%BA%D0%B0%D1%8F_%D1%88%D0%BA%D0%BE%D0%BB%D0%B0" title="Афінская школа">Афінская школа</a>» работы <a href="/wiki/%D0%A0%D0%B0%D1%84%D0%B0%D1%8D%D0%BB%D1%8C_%D0%A1%D0%B0%D0%BD%D1%86%D1%96" title="Рафаэль Санці">Рафаэля Санці</a>.</figcaption></figure> <p>Складаныя задачы ўмелі рашаць у пачатку <a href="/w/index.php?title=2_%D1%82%D1%8B%D1%81%D1%8F%D1%87%D0%B0%D0%B3%D0%BE%D0%B4%D0%B4%D0%B7%D1%8F_%D0%B4%D0%B0_%D0%BD.%D1%8D.&action=edit&redlink=1" class="new" title="2 тысячагоддзя да н.э. (няма такой старонкі)">2 тысячагоддзя да н.э.</a> у старажытным <a href="/wiki/%D0%92%D0%B0%D0%B2%D1%96%D0%BB%D0%BE%D0%BD" title="Вавілон">Вавілоне</a>: у матэматычных тэкстах, напісаных <a href="/wiki/%D0%9A%D0%BB%D1%96%D0%BD%D0%B0%D0%BF%D1%96%D1%81" title="Клінапіс">клінапісам</a> на гліняных таблічках, ёсць квадратныя і <a href="/w/index.php?title=%D0%91%D1%96%D0%BA%D0%B2%D0%B0%D0%B4%D1%80%D0%B0%D1%82%D0%BD%D1%8B%D1%8F_%D1%9E%D1%80%D0%B0%D1%9E%D0%BD%D0%B5%D0%BD%D0%BD%D1%96&action=edit&redlink=1" class="new" title="Біквадратныя ўраўненні (няма такой старонкі)">біквадратныя ўраўненні</a>, <a href="/wiki/%D0%A1%D1%96%D1%81%D1%82%D1%8D%D0%BC%D0%B0_%D0%BB%D1%96%D0%BD%D0%B5%D0%B9%D0%BD%D1%8B%D1%85_%D0%B0%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0%D1%96%D1%87%D0%BD%D1%8B%D1%85_%D1%83%D1%80%D0%B0%D1%9E%D0%BD%D0%B5%D0%BD%D0%BD%D1%8F%D1%9E" title="Сістэма лінейных алгебраічных ураўненняў">сістэмы ўраўненняў з дзвюма невядомымі</a> і найпрасцейшыя <a href="/w/index.php?title=%D0%9A%D1%83%D0%B1%D1%96%D1%87%D0%BD%D1%8B%D1%8F_%D1%9E%D1%80%D0%B0%D1%9E%D0%BD%D0%B5%D0%BD%D0%BD%D1%96&action=edit&redlink=1" class="new" title="Кубічныя ўраўненні (няма такой старонкі)">кубічныя ўраўненні</a>. Пры гэтым вавіланяне не выкарыстоўвалі літарных абазначэнняў, а прыводзілі рашэнні тыповых задач, зводзячы рашэнне аналагічных задач да замены лікавых значэнняў. У лікавай форме прыводзіліся таксама і некаторыя правілы <a href="/w/index.php?title=%D0%A2%D0%BE%D0%B5%D1%81%D0%BD%D1%8B%D1%8F_%D0%BF%D0%B5%D1%80%D0%B0%D1%9E%D1%82%D0%B2%D0%B0%D1%80%D1%8D%D0%BD%D0%BD%D1%96&action=edit&redlink=1" class="new" title="Тоесныя пераўтварэнні (няма такой старонкі)">тоесных пераўтварэнняў</a>. Калі пры рашэнні ўраўнення трэба было знайсці <a href="/wiki/%D0%9A%D0%B2%D0%B0%D0%B4%D1%80%D0%B0%D1%82%D0%BD%D1%8B_%D0%BA%D0%BE%D1%80%D0%B0%D0%BD%D1%8C" title="Квадратны корань">квадратны корань</a> ліку <i>a</i>, які не з’яўляецца дакладным квадратам, прыбліжанае значэнне кораня <i>x</i> знаходзілі як <a href="/wiki/%D0%A1%D1%8F%D1%80%D1%8D%D0%B4%D0%BD%D1%8F%D0%B5_%D0%B0%D1%80%D1%8B%D1%84%D0%BC%D0%B5%D1%82%D1%8B%D1%87%D0%BD%D0%B0%D0%B5" title="Сярэдняе арыфметычнае">сярэдняе арыфметычнае</a> лікаў <i>х</i> і <i>а/х</i>. </p><p>Першыя агульныя сцвярджэнні аб тоесных пераўтварэннях сустракаюцца ў старажытнагрэчаскіх матэматыкаў, пачынаючы з <a href="/wiki/6_%D1%81%D1%82%D0%B0%D0%B3%D0%BE%D0%B4%D0%B4%D0%B7%D0%B5_%D0%B4%D0%B0_%D0%BD.%D1%8D." class="mw-redirect" title="6 стагоддзе да н.э.">VI стагоддзя да н.э.</a> Сярод матэматыкаў <a href="/wiki/%D0%A1%D1%82%D0%B0%D1%80%D0%B0%D0%B6%D1%8B%D1%82%D0%BD%D0%B0%D1%8F_%D0%93%D1%80%D1%8D%D1%86%D1%8B%D1%8F" title="Старажытная Грэцыя">старажытнай Грэцыі</a> было прынята прадстаўляць усе алгебраічныя сцвярджэнні ў геаметрычнай форме. Замест <a href="/wiki/%D0%A1%D0%BA%D0%BB%D0%B0%D0%B4%D0%B0%D0%BD%D0%BD%D0%B5" title="Складанне">складання</a> лікаў казалі аб складанні <a href="/wiki/%D0%90%D0%B4%D1%80%D1%8D%D0%B7%D0%B0%D0%BA" title="Адрэзак">адрэзкаў</a>, <a href="/wiki/%D0%97%D0%B4%D0%B0%D0%B1%D1%8B%D1%82%D0%B0%D0%BA" class="mw-redirect" title="Здабытак">здабытак</a> двух лікаў вытлумачвалі як <a href="/wiki/%D0%9F%D0%BB%D0%BE%D1%88%D1%87%D0%B0" title="Плошча">плошчу</a> <a href="/wiki/%D0%9F%D1%80%D0%B0%D0%BC%D0%B0%D0%B2%D1%83%D0%B3%D0%BE%D0%BB%D1%8C%D0%BD%D1%96%D0%BA" title="Прамавугольнік">прамавугольніка</a>, а здабытак трох лікаў як <a href="/wiki/%D0%90%D0%B1%27%D1%91%D0%BC" class="mw-redirect" title="Аб'ём">аб'ём</a> прамавугольнага <a href="/wiki/%D0%9F%D0%B0%D1%80%D0%B0%D0%BB%D0%B5%D0%BB%D0%B5%D0%BF%D1%96%D0%BF%D0%B5%D0%B4" title="Паралелепіпед">паралелепіпеда</a>. Алгебраічныя формулы прымалі выгляд <a href="/w/index.php?title=%D0%A1%D1%83%D0%B0%D0%B4%D0%BD%D0%BE%D1%81%D1%96%D0%BD%D1%8B&action=edit&redlink=1" class="new" title="Суадносіны (няма такой старонкі)">суадносін</a> паміж плошчамі і аб’ёмамі. Напрыклад, казалі, што плошча <a href="/wiki/%D0%9A%D0%B2%D0%B0%D0%B4%D1%80%D0%B0%D1%82" title="Квадрат">квадрата</a>, пабудаванага на суме двух адрэзкаў, роўная суме плошчаў квадратаў, пабудаваных на гэтых адрэзках, павялічанай на падвоеную плошчу прамавугольніка, пабудаванага на гэтых адрэзках. Такім чынам з’явіліся тэрміны «квадрат ліку», што азначае здабытак велічыні на сябе, «куб ліку», «<a href="/wiki/%D0%A1%D1%8F%D1%80%D1%8D%D0%B4%D0%BD%D1%8F%D0%B5_%D0%B3%D0%B5%D0%B0%D0%BC%D0%B5%D1%82%D1%80%D1%8B%D1%87%D0%BD%D0%B0%D0%B5" title="Сярэдняе геаметрычнае">сярэдняе геаметрычнае</a>». Геаметрычную форму ў грэкаў набыло рашэнне квадратнага раўнення — яны шукалі значэнне стараны прамавугольніка па зададзенаму <a href="/wiki/%D0%9F%D0%B5%D1%80%D1%8B%D0%BC%D0%B5%D1%82%D1%80" title="Перыметр">перыметру</a> і плошчы. </p><p>Большасць задач у Грэцыі рашалася шляхам <a href="/w/index.php?title=%D0%9F%D0%B0%D0%B1%D1%83%D0%B4%D0%BE%D0%B2%D0%B0_%D0%B7_%D0%B4%D0%B0%D0%BF%D0%B0%D0%BC%D0%BE%D0%B3%D0%B0%D0%B9_%D1%86%D1%8B%D1%80%D0%BA%D1%83%D0%BB%D1%8F_%D1%96_%D0%BB%D1%96%D0%BD%D0%B5%D0%B9%D0%BA%D1%96&action=edit&redlink=1" class="new" title="Пабудова з дапамогай цыркуля і лінейкі (няма такой старонкі)">пабудоў цыркулем і лінейкай</a>. Але не ўсе задачы можна было рашыць такім метадам. Прыкладамі такіх задач з’яўляюцца <a href="/w/index.php?title=%D0%9F%D0%B0%D0%B4%D0%B2%D0%B0%D0%B5%D0%BD%D0%BD%D0%B5_%D0%BA%D1%83%D0%B1%D0%B0&action=edit&redlink=1" class="new" title="Падваенне куба (няма такой старонкі)">падваенне куба</a>, <a href="/w/index.php?title=%D0%A2%D1%80%D1%8B%D1%81%D0%B5%D0%BA%D1%86%D1%8B%D1%8F_%D0%B2%D1%83%D0%B3%D0%BB%D0%B0&action=edit&redlink=1" class="new" title="Трысекцыя вугла (няма такой старонкі)">трысекцыя вугла</a>, задача пабудовы правільнага сямівугольніка. Усе яны зводзіліся да кубічных ураўненняў выгляду <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x^{3}=2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mo>=</mo> <mn>2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x^{3}=2}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/18dca2845d7b13d4fdf8f6f53e8e74c64838fef0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.645ex; height:2.676ex;" alt="{\displaystyle x^{3}=2}"></span>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 4x^{3}-3x=a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>4</mn> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mo>−</mo> <mn>3</mn> <mi>x</mi> <mo>=</mo> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 4x^{3}-3x=a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/50d55c657699e7f343b30859b2532ad36257a6b6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:13.207ex; height:2.843ex;" alt="{\displaystyle 4x^{3}-3x=a}"></span> і <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x^{3}+x^{2}-2x-1=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mn>2</mn> <mi>x</mi> <mo>−</mo> <mn>1</mn> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x^{3}+x^{2}-2x-1=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ad84c9e1f879abe5eb9723a4b44037a8566b84ee" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:21.205ex; height:2.843ex;" alt="{\displaystyle x^{3}+x^{2}-2x-1=0}"></span> адпаведна. Для рашэння гэтых задач быў распрацаваны новы метад, — адшуканне кропак перасячэння <a href="/wiki/%D0%9A%D0%B0%D0%BD%D1%96%D1%87%D0%BD%D0%B0%D0%B5_%D1%81%D1%8F%D1%87%D1%8D%D0%BD%D0%BD%D0%B5" title="Канічнае сячэнне">канічных сячэнняў</a> (<a href="/wiki/%D0%AD%D0%BB%D1%96%D0%BF%D1%81" title="Эліпс">эліпса</a>, <a href="/wiki/%D0%9F%D0%B0%D1%80%D0%B0%D0%B1%D0%B0%D0%BB%D0%B0" title="Парабала">парабалы</a> і <a href="/wiki/%D0%93%D1%96%D0%BF%D0%B5%D1%80%D0%B1%D0%B0%D0%BB%D0%B0_(%D0%BC%D0%B0%D1%82%D1%8D%D0%BC%D0%B0%D1%82%D1%8B%D0%BA%D0%B0)" title="Гіпербала (матэматыка)">гіпербалы</a>). </p> <figure typeof="mw:File/Thumb"><a href="/wiki/%D0%A4%D0%B0%D0%B9%D0%BB:Aryabhata.jpeg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/31/Aryabhata.jpeg/200px-Aryabhata.jpeg" decoding="async" width="200" height="238" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/3/31/Aryabhata.jpeg 1.5x" data-file-width="229" data-file-height="273" /></a><figcaption>Старажытнаіндыйскі матэматык <a href="/wiki/%D0%90%D1%80%D1%8B%D1%8F%D0%B1%D1%85%D0%B0%D1%82%D0%B0_I" class="mw-redirect" title="Арыябхата I">Арыябхата I</a>.</figcaption></figure> <p>Геаметрычны падыход да алгебраічных праблем абмяжоўваў далейшае развіццё навукі. Напрыклад, можна было складаць велічыні аднолькавай размернасці (<a href="/wiki/%D0%94%D0%B0%D1%9E%D0%B6%D1%8B%D0%BD%D1%8F" title="Даўжыня">даўжыні</a>, <a href="/wiki/%D0%9F%D0%BB%D0%BE%D1%88%D1%87%D0%B0" title="Плошча">плошчы</a>, <a href="/wiki/%D0%90%D0%B1%27%D1%91%D0%BC" class="mw-redirect" title="Аб'ём">аб'ёмы</a>), але нельга было казаць пра здабыткі больш чым трох <a href="/wiki/%D0%9C%D0%BD%D0%BE%D0%B6%D0%B0%D0%BD%D0%BD%D0%B5" title="Множанне">множнікаў</a>, бо не было паняцця чатырохмернага аб’ёму. Спробы адмовіцца ад геаметрычнай трактоўкі з’явілася ў <a href="/wiki/%D0%94%D1%8B%D1%8F%D1%84%D0%B0%D0%BD%D1%82_%D0%90%D0%BB%D0%B5%D0%BA%D1%81%D0%B0%D0%BD%D0%B4%D1%80%D1%8B%D0%B9%D1%81%D0%BA%D1%96" title="Дыяфант Александрыйскі">Дыяфанта Александрыйскага</a>, які жыў у <a href="/wiki/3_%D1%81%D1%82%D0%B0%D0%B3%D0%BE%D0%B4%D0%B4%D0%B7%D0%B5" class="mw-redirect" title="3 стагоддзе">III стагоддзі</a>. У яго кнізе «Арыфметыка» з’яўляецца літарная сімволіка і спецыяльныя абазначэнні для <a href="/wiki/%D0%A1%D1%82%D1%83%D0%BF%D0%B5%D0%BD%D1%8F%D0%B2%D0%B0%D0%BD%D0%BD%D0%B5" title="Ступеняванне">ступеней</a> да 6-й. Былі ў яго і абазначэнні для адмоўных ступеней, <a href="/wiki/%D0%90%D0%B4%D0%BC%D0%BE%D1%9E%D0%BD%D1%8B%D1%8F_%D0%BB%D1%96%D0%BA%D1%96" class="mw-redirect" title="Адмоўныя лікі">адмоўных лікаў</a>, а таксама <a href="/w/index.php?title=%D0%97%D0%BD%D0%B0%D0%BA_%D1%80%D0%BE%D1%9E%D0%BD%D0%B0%D1%81%D1%86%D1%96&action=edit&redlink=1" class="new" title="Знак роўнасці (няма такой старонкі)">знак роўнасці</a> (адмысловага знака для складання яшчэ не было), кароткі запіс правіл множання дадатных і адмоўных лікаў. На далейшае развіццё алгебры істотна паўплывалі даследаваныя Дыяфантам задачы, якія прыводзяць да складаных сістэм алгебраічных ураўненняў, у тым ліку да сістэм, дзе колькасць ураўненняў была меншай за колькасць невядомых. Для такіх ураўненняў Дыяфант шукаў толькі дадатныя <a href="/wiki/%D0%A0%D0%B0%D1%86%D1%8B%D1%8F%D0%BD%D0%B0%D0%BB%D1%8C%D0%BD%D1%8B%D1%8F_%D0%BB%D1%96%D0%BA%D1%96" class="mw-redirect" title="Рацыянальныя лікі">рацыянальныя</a> рашэнні. </p><p>З <a href="/wiki/6_%D1%81%D1%82%D0%B0%D0%B3%D0%BE%D0%B4%D0%B4%D0%B7%D0%B5" class="mw-redirect" title="6 стагоддзе">VI стагоддзя</a> цэнтр матэматычных даследаванняў перамясціўся ў <a href="/wiki/%D0%86%D0%BD%D0%B4%D1%8B%D1%8F" title="Індыя">Індыю</a>, <a href="/wiki/%D0%9A%D1%96%D1%82%D0%B0%D0%B9" title="Кітай">Кітай</a>, краіны <a href="/wiki/%D0%91%D0%BB%D1%96%D0%B7%D0%BA%D1%96_%D0%A3%D1%81%D1%85%D0%BE%D0%B4" title="Блізкі Усход">Блізкага Усходу</a> і <a href="/wiki/%D0%A1%D1%8F%D1%80%D1%8D%D0%B4%D0%BD%D1%8F%D1%8F_%D0%90%D0%B7%D1%96%D1%8F" title="Сярэдняя Азія">Сярэдняй Азіі</a>. Кітайскія навукоўцы распрацавалі метад паслядоўнага <a href="/w/index.php?title=%D0%92%D1%8B%D0%BA%D0%BB%D1%8E%D1%87%D1%8D%D0%BD%D0%BD%D0%B5_%D0%BD%D0%B5%D0%B2%D1%8F%D0%B4%D0%BE%D0%BC%D1%8B%D1%85&action=edit&redlink=1" class="new" title="Выключэнне невядомых (няма такой старонкі)">выключэння невядомых</a> для рашэння сістэм лінейных ураўненняў, далі новыя метады прыбліжанага рашэння ўраўненняў вышэйшых ступеней. Індыйскія матэматыкі, а іменна <a href="/wiki/%D0%90%D1%80%D1%8B%D1%8F%D0%B1%D1%85%D0%B0%D1%82%D0%B0_I" class="mw-redirect" title="Арыябхата I">Арыябхата I</a>, <a href="/wiki/%D0%91%D1%80%D0%B0%D0%BC%D0%B0%D0%B3%D1%83%D0%BF%D1%82%D0%B0" class="mw-redirect" title="Брамагупта">Брамагупта</a>, выкарыстоўвалі <a href="/wiki/%D0%90%D0%B4%D0%BC%D0%BE%D1%9E%D0%BD%D1%8B_%D0%BB%D1%96%D0%BA" title="Адмоўны лік">адмоўныя лікі</a>, удасканалілі літарную сімволіку. Але толькі ў працах вучоных Блізкага Усходу і Сярэдняй Азіі алгебра аформілася ў самастойную галіну матэматыкі, якая займаецца рашэннем ураўненняў. У <a href="/wiki/9_%D1%81%D1%82%D0%B0%D0%B3%D0%BE%D0%B4%D0%B4%D0%B7%D0%B5" class="mw-redirect" title="9 стагоддзе">IX стагоддзі</a> ўзбекскі матэматык і <a href="/wiki/%D0%90%D1%81%D1%82%D1%80%D0%B0%D0%BD%D0%BE%D0%BC" title="Астраном">астраном</a> <a href="/wiki/%D0%9C%D1%83%D1%85%D0%B0%D0%BC%D0%B5%D0%B4_%D0%B0%D0%BB%D1%8C-%D0%A5%D0%B0%D1%80%D1%8D%D0%B7%D0%BC" class="mw-redirect" title="Мухамед аль-Харэзм">Мухамед аль-Харэзм</a> напісаў трактат «Кітаб аль-джэбр Валь-мукабала», дзе даў агульныя правілы для рашэння ўраўненняў першай ступені. Слова «аль-джэбр» (аднаўленне), ад якога новая навука атрымала сваю назву, азначала перанос адмоўных складнікаў ураўнення з адной часткі ў іншую са зменай знака. Навукоўцы Усходу вывучалі рашэнне кубічных ураўненняў, аднак не здолелі атрымаць агульнай формулы для іхніх каранёў. </p><p>У <a href="/wiki/%D0%95%D1%9E%D1%80%D0%BE%D0%BF%D0%B0" title="Еўропа">Еўропе</a> вывучэнне алгебры пачалося ў <a href="/wiki/13_%D1%81%D1%82%D0%B0%D0%B3%D0%BE%D0%B4%D0%B4%D0%B7%D0%B5" class="mw-redirect" title="13 стагоддзе">XIII стагоддзі</a>. Адным з буйных матэматыкаў гэтага часу быў італьянец <a href="/wiki/%D0%A4%D1%96%D0%B1%D0%B0%D0%BD%D0%B0%D1%87%D1%8B" title="Фібаначы">Леанарда Пізанскі</a>, вядомы па мянушцы Фібаначы. Яго «<a href="/w/index.php?title=%D0%9A%D0%BD%D1%96%D0%B3%D0%B0_%D0%B0%D0%B1%D0%B0%D0%BA%D0%B0&action=edit&redlink=1" class="new" title="Кніга абака (няма такой старонкі)">Кніга абака</a>» <a href="/wiki/1202" title="1202">1202</a> года ўяўляе сабой трактат са звесткамі па арыфметыцы і алгебры, у тым ліку і пра квадратныя ураўненні. Першым значным самастойным дасягненнем заходнееўрапейскіх вучоных стала адкрыццё <a href="/w/index.php?title=%D0%A4%D0%BE%D1%80%D0%BC%D1%83%D0%BB%D0%B0_%D0%9A%D0%B0%D1%80%D0%B4%D0%B0%D0%BD%D0%B0&action=edit&redlink=1" class="new" title="Формула Кардана (няма такой старонкі)">формулы для каранёў кубічнага ўраўнення</a>, апублікаванай у <a href="/wiki/1545" title="1545">1545</a> годзе. Гэта было заслугай італьянскіх алгебраістаў <a href="/w/index.php?title=%D0%A1%D1%86%D1%8B%D0%BF%D1%96%D1%91%D0%BD_%D0%B4%D1%8D%D0%BB%D1%8C_%D0%A4%D0%B5%D1%80%D0%B0&action=edit&redlink=1" class="new" title="Сцыпіён дэль Фера (няма такой старонкі)">Сцыпіёна дэль Фера</a>, <a href="/wiki/%D0%9D%D1%96%D0%BA%D0%BE%D0%BB%D0%B0_%D0%A2%D0%B0%D1%80%D1%82%D0%B0%D0%BB%D1%8C%D1%8F" title="Нікола Тарталья">Ніколы Тартальі</a> і <a href="/w/index.php?title=%D0%94%D0%B6%D1%8B%D1%80%D0%B0%D0%BB%D0%B0%D0%BC%D0%B0_%D0%9A%D0%B0%D1%80%D0%B4%D0%B0%D0%BD%D0%B0&action=edit&redlink=1" class="new" title="Джыралама Кардана (няма такой старонкі)">Джыралама Кардана</a>. Вучань Кардана <a href="/w/index.php?title=%D0%9B%D0%B0%D0%B4%D0%B0%D0%B2%D1%96%D0%BA%D0%B0_%D0%A4%D0%B5%D1%80%D0%B0%D1%80%D1%8B&action=edit&redlink=1" class="new" title="Ладавіка Ферары (няма такой старонкі)">Ладавіка Ферары</a> рашыў і <a href="/w/index.php?title=%D0%A3%D1%80%D0%B0%D1%9E%D0%BD%D0%B5%D0%BD%D0%BD%D0%B5_%D1%87%D0%B0%D1%86%D0%B2%D1%91%D1%80%D1%82%D0%B0%D0%B9_%D1%81%D1%82%D1%83%D0%BF%D0%B5%D0%BD%D1%96&action=edit&redlink=1" class="new" title="Ураўненне чацвёртай ступені (няма такой старонкі)">ўраўненне 4-й ступені</a>. Вывучэнне некаторых пытанняў, звязаных з каранямі кубічных ураўненняў, прывяло італьянскага алгебраіста <a href="/w/index.php?title=%D0%A0%D0%B0%D1%84%D0%B0%D1%8D%D0%BB%D1%8C_%D0%91%D0%B0%D0%BC%D0%B1%D0%B5%D0%BB%D1%96&action=edit&redlink=1" class="new" title="Рафаэль Бамбелі (няма такой старонкі)">Рафаэля Бамбелі</a> да адкрыцця <a href="/wiki/%D0%9A%D0%B0%D0%BC%D0%BF%D0%BB%D0%B5%D0%BA%D1%81%D0%BD%D1%8B_%D0%BB%D1%96%D0%BA" title="Камплексны лік">камплексных лікаў</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Развіццё_сімволікі"><span id=".D0.A0.D0.B0.D0.B7.D0.B2.D1.96.D1.86.D1.86.D1.91_.D1.81.D1.96.D0.BC.D0.B2.D0.BE.D0.BB.D1.96.D0.BA.D1.96"></span>Развіццё сімволікі</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0&veaction=edit&section=4" title="Правіць раздзел: Развіццё сімволікі" class="mw-editsection-visualeditor"><span>правіць</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0&action=edit&section=4" title="Правіць зыходнік раздзела: Развіццё сімволікі"><span>правіць зыходнік</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/%D0%A4%D0%B0%D0%B9%D0%BB:Jer%C3%B4me_Cardan.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/97/Jer%C3%B4me_Cardan.jpg/200px-Jer%C3%B4me_Cardan.jpg" decoding="async" width="200" height="260" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/9/97/Jer%C3%B4me_Cardan.jpg 1.5x" data-file-width="280" data-file-height="364" /></a><figcaption>У <a href="/wiki/1545" title="1545">1545</a> годзе італьянскі матэматык <a href="/w/index.php?title=%D0%94%D0%B6%D1%8B%D1%80%D0%B0%D0%BB%D0%B0%D0%BC%D0%B0_%D0%9A%D0%B0%D1%80%D0%B4%D0%B0%D0%BD%D0%B0&action=edit&redlink=1" class="new" title="Джыралама Кардана (няма такой старонкі)">Джыралама Кардана</a> апублікаваў сваю працу «<a href="/w/index.php?title=Ars_Magna&action=edit&redlink=1" class="new" title="Ars Magna (няма такой старонкі)">Ars Magna</a>», у якой ён упершыню прапанаваў метад рашэння агульнага ўраўнення чацвёртай ступені.</figcaption></figure> <p>Адсутнасць зручнай і развітой сімволікі стрымлівала далейшае развіццё алгебры: самыя складаныя формулы даводзілася апісваць словамі. У канцы <a href="/wiki/15_%D1%81%D1%82%D0%B0%D0%B3%D0%BE%D0%B4%D0%B4%D0%B7%D0%B5" class="mw-redirect" title="15 стагоддзе">XV стагоддзя</a> <a href="/wiki/%D0%9B%D1%83%D0%BA%D0%B0_%D0%9F%D0%B0%D1%87%D0%BE%D0%BB%D1%96" title="Лука Пачолі">Лука Пачолі</a> зрабіў спробу ўвесці алгебраічную сімволіку, аднак большага поспеху ў гэтай справе дасягнуў у канцы <a href="/wiki/16_%D1%81%D1%82%D0%B0%D0%B3%D0%BE%D0%B4%D0%B4%D0%B7%D0%B5" class="mw-redirect" title="16 стагоддзе">XVI стагоддзя</a> французскі <a href="/wiki/%D0%9C%D0%B0%D1%82%D1%8D%D0%BC%D0%B0%D1%82%D1%8B%D0%BA" title="Матэматык">матэматык</a> <a href="/wiki/%D0%A4%D1%80%D0%B0%D0%BD%D1%81%D1%83%D0%B0_%D0%92%D1%96%D0%B5%D1%82" title="Франсуа Віет">Франсуа Віет</a>, які ўвёў літарныя абазначэнні не толькі для невядомых, але і для адвольных сталых велічынь. Сімволіка Віета была ўдасканалена яго паслядоўнікамі. Канчатковы выгляд ёй надаў у <a href="/wiki/17_%D1%81%D1%82%D0%B0%D0%B3%D0%BE%D0%B4%D0%B4%D0%B7%D0%B5" class="mw-redirect" title="17 стагоддзе">XVII стагоддзі</a> французскі <a href="/wiki/%D0%A4%D1%96%D0%BB%D0%BE%D1%81%D0%B0%D1%84" title="Філосаф">філосаф</a> і матэматык <a href="/wiki/%D0%A0%D1%8D%D0%BD%D1%8D_%D0%94%D1%8D%D0%BA%D0%B0%D1%80%D1%82" title="Рэнэ Дэкарт">Рэнэ Дэкарт</a>, які ўвёў абазначэнні для паказчыкаў ступеней, якія прымяняюцца да гэтага часу. </p><p>Паступова пашыраўся запас лікаў, з якімі можна было выконваць дзеянні. Пачалі шырока ўжывацца адмоўныя лікі, затым — <a href="/wiki/%D0%9A%D0%B0%D0%BC%D0%BF%D0%BB%D0%B5%D0%BA%D1%81%D0%BD%D1%8B_%D0%BB%D1%96%D0%BA" title="Камплексны лік">камплексныя</a>, навукоўцы сталі свабодна выкарыстоўваць <a href="/wiki/%D0%86%D1%80%D0%B0%D1%86%D1%8B%D1%8F%D0%BD%D0%B0%D0%BB%D1%8C%D0%BD%D1%8B_%D0%BB%D1%96%D0%BA" title="Ірацыянальны лік">ірацыянальныя лікі</a>. Аказалася, што, нягледзячы на такое пашырэнне запасу лікаў, устаноўленыя раней правілы алгебраічных пераўтварэнняў захоўваюць сваю сілу. Нарэшце, Дэкарт здолеў вызваліць алгебру ад неўласцівай ёй геаметрычнай формы. Усё гэта дало магчымасць разглядаць пытанне рашэння ўраўненняў у самым агульным выглядзе, рашаць геаметрычныя задачы з дапамогай ураўненняў. Напрыклад, задача аб знаходжанні пункта перасячэння дзвюх прамых звялася да рашэння сістэмы ўраўненняў, якім задавальнялі пункты гэтых прамых. Такі падыход да рашэння геаметрычных задач атрымаў назву <a href="/wiki/%D0%90%D0%BD%D0%B0%D0%BB%D1%96%D1%82%D1%8B%D1%87%D0%BD%D0%B0%D1%8F_%D0%B3%D0%B5%D0%B0%D0%BC%D0%B5%D1%82%D1%80%D1%8B%D1%8F" title="Аналітычная геаметрыя">аналітычнай геаметрыі</a>. </p><p>Развіццё алфавітнай сімволікі дазволіла ўстанавіць агульныя сцвярджэнні адносна ўраўненняў: <a href="/wiki/%D0%A2%D1%8D%D0%B0%D1%80%D1%8D%D0%BC%D0%B0_%D0%91%D0%B5%D0%B7%D1%83" title="Тэарэма Безу">тэарэма Безу</a> аб <a href="/wiki/%D0%94%D0%B7%D1%8F%D0%BB%D1%96%D0%BC%D0%B0%D1%81%D1%86%D1%8C" title="Дзялімасць">дзялімасці</a> <a href="/wiki/%D0%9C%D0%BD%D0%B0%D0%B3%D0%B0%D1%87%D0%BB%D0%B5%D0%BD" title="Мнагачлен">мнагачлена</a> <span style="white-space: nowrap; font-family: times, serif, palatino linotype, new athena unicode, athena, gentium, code2000; font-size: 120%;"><i>P</i>(<i>х</i>)</span> на двухчлен <span style="white-space: nowrap; font-family: times, serif, palatino linotype, new athena unicode, athena, gentium, code2000; font-size: 120%;">(<i>х</i> — <i>а</i>)</span>, дзе <span style="white-space: nowrap; font-family: times, serif, palatino linotype, new athena unicode, athena, gentium, code2000; font-size: 120%;"><i>a</i></span> ёсць <a href="/wiki/%D0%9A%D0%BE%D1%80%D0%B0%D0%BD%D1%8C_%D0%BC%D0%BD%D0%B0%D0%B3%D0%B0%D1%87%D0%BB%D0%B5%D0%BD%D0%B0" title="Корань мнагачлена">корань гэтага мнагачлена</a>, <a href="/w/index.php?title=%D0%A4%D0%BE%D1%80%D0%BC%D1%83%D0%BB%D0%B0_%D0%92%D1%96%D0%B5%D1%82%D0%B0&action=edit&redlink=1" class="new" title="Формула Віета (няма такой старонкі)">формула Віета</a> для суадносін паміж каранямі квадратнага ўраўнення і яго каэфіцыентамі; правілы, якія дазваляюць ацэньваць колькасць рэчаісных каранёў ураўнення, агульныя метады выключэння невядомых з сістэмы ўраўненняў і г. д. </p> <div class="mw-heading mw-heading3"><h3 id="Далейшыя_поспехі"><span id=".D0.94.D0.B0.D0.BB.D0.B5.D0.B9.D1.88.D1.8B.D1.8F_.D0.BF.D0.BE.D1.81.D0.BF.D0.B5.D1.85.D1.96"></span>Далейшыя поспехі</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0&veaction=edit&section=5" title="Правіць раздзел: Далейшыя поспехі" class="mw-editsection-visualeditor"><span>правіць</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0&action=edit&section=5" title="Правіць зыходнік раздзела: Далейшыя поспехі"><span>правіць зыходнік</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Асабліва далёка ў сферы рашэння <a href="/wiki/%D0%A1%D1%96%D1%81%D1%82%D1%8D%D0%BC%D0%B0_%D0%BB%D1%96%D0%BD%D0%B5%D0%B9%D0%BD%D1%8B%D1%85_%D0%B0%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0%D1%96%D1%87%D0%BD%D1%8B%D1%85_%D1%83%D1%80%D0%B0%D1%9E%D0%BD%D0%B5%D0%BD%D0%BD%D1%8F%D1%9E" title="Сістэма лінейных алгебраічных ураўненняў">сістэмы лінейных ураўненняў</a> удалося прасунуцца ў <a href="/wiki/18_%D1%81%D1%82%D0%B0%D0%B3%D0%BE%D0%B4%D0%B4%D0%B7%D0%B5" class="mw-redirect" title="18 стагоддзе">XVIII стагоддзі</a>, для іх былі атрыманы формулы, якія дазваляюць выразіць рашэнне праз каэфіцыенты і свабодныя складнікі. Далейшае вывучэнне такіх сістэм ураўненняў прывяло да <a href="/w/index.php?title=%D0%A2%D1%8D%D0%BE%D1%80%D1%8B%D1%8F_%D0%BC%D0%B0%D1%82%D1%80%D1%8B%D1%86&action=edit&redlink=1" class="new" title="Тэорыя матрыц (няма такой старонкі)">тэорыі</a> <a href="/wiki/%D0%9C%D0%B0%D1%82%D1%80%D1%8B%D1%86%D0%B0_(%D0%BC%D0%B0%D1%82%D1%8D%D0%BC%D0%B0%D1%82%D1%8B%D0%BA%D0%B0)" title="Матрыца (матэматыка)">матрыц</a> і <a href="/wiki/%D0%92%D1%8B%D0%B7%D0%BD%D0%B0%D1%87%D0%BD%D1%96%D0%BA_(%D0%B0%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0)" title="Вызначнік (алгебра)">вызначнікаў</a>. У канцы <a href="/wiki/18_%D1%81%D1%82%D0%B0%D0%B3%D0%BE%D0%B4%D0%B4%D0%B7%D0%B5" class="mw-redirect" title="18 стагоддзе">XVIII стагоддзя</a> было даказана, што любое алгебраічнае ўраўненне з камплекснымі каэфіцыентамі мае хаця б адзін камплексны корань. Гэта сцвярджэнне называецца <a href="/wiki/%D0%90%D1%81%D0%BD%D0%BE%D1%9E%D0%BD%D0%B0%D1%8F_%D1%82%D1%8D%D0%B0%D1%80%D1%8D%D0%BC%D0%B0_%D0%B0%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D1%8B" title="Асноўная тэарэма алгебры">асноўнай тэарэмай алгебры</a>. На працягу двух з паловай стагоддзяў увага алгебраістаў была прыкавана да задачы аб вывадзе формулы для рашэння агульнага ўраўнення 5-й ступені. Трэба было выразіць рашэнне гэтага ўраўнення праз яго каэфіцыенты з дапамогай арыфметычных аперацый і каранёў, гэта значыць развязаць ураўненне ў радыкалах. Толькі ў <a href="/wiki/19_%D1%81%D1%82%D0%B0%D0%B3%D0%BE%D0%B4%D0%B4%D0%B7%D0%B5" class="mw-redirect" title="19 стагоддзе">XIX стагоддзі</a> <a href="/wiki/%D0%86%D1%82%D0%B0%D0%BB%D1%8C%D1%8F%D0%BD%D0%B5%D1%86" class="mw-redirect" title="Італьянец">італьянец</a> <a href="/wiki/%D0%9F%D0%B0%D0%BE%D0%BB%D0%B0_%D0%A0%D1%83%D1%84%D1%96%D0%BD%D1%96" title="Паола Руфіні">Паола Руфіні</a> і <a href="/w/index.php?title=%D0%9D%D0%B0%D1%80%D0%B2%D0%B5%D0%B6%D0%B0%D1%86&action=edit&redlink=1" class="new" title="Нарвежац (няма такой старонкі)">нарвежац</a> <a href="/wiki/%D0%9D%D1%96%D0%BB%D1%8C%D1%81_%D0%A5%D0%B5%D0%BD%D1%80%D1%8B%D0%BA_%D0%90%D0%B1%D0%B5%D0%BB%D1%8C" title="Нільс Хенрык Абель">Нільс Абель</a> незалежна адзін ад аднаго даказалі, што такія формулы не існуюць (гл. <a href="/w/index.php?title=%D0%A2%D1%8D%D0%B0%D1%80%D1%8D%D0%BC%D0%B0_%D0%90%D0%B1%D0%B5%D0%BB%D1%8F-%D0%A0%D1%83%D1%84%D1%96%D0%BD%D1%96&action=edit&redlink=1" class="new" title="Тэарэма Абеля-Руфіні (няма такой старонкі)">Тэарэма Абеля-Руфіні</a>). Гэтыя даследаванні былі завершаны французскім матэматыкам <a href="/wiki/%D0%AD%D0%B2%D0%B0%D1%80%D1%8B%D1%81%D1%82_%D0%93%D0%B0%D0%BB%D1%83%D0%B0" title="Эварыст Галуа">Эварытсам Галуа</a>, чые метады дазволілі для гэтага ўраўнення вызначыць, развязваецца яно ў радыкалах ці не. Адзін з самых выдатных матэматыкаў у гісторыі <a href="/wiki/%D0%9A%D0%B0%D1%80%D0%BB_%D0%A4%D1%80%D1%8B%D0%B4%D1%80%D1%8B%D1%85_%D0%93%D0%B0%D1%83%D1%81" title="Карл Фрыдрых Гаус">Карл Фрыдрых Гаус</a> высвятліў, калі можна пабудаваць <a href="/wiki/%D0%A6%D1%8B%D1%80%D0%BA%D1%83%D0%BB%D1%8C" title="Цыркуль">цыркулем</a> і лінейкай правільны <span style="white-space: nowrap; font-family: times, serif, palatino linotype, new athena unicode, athena, gentium, code2000; font-size: 120%;"><i>n</i></span>-вугольнік: дадзеная задача была напрамую звязана з вывучэннем каранёў ураўнення <span style="white-space: nowrap; font-family: times, serif, palatino linotype, new athena unicode, athena, gentium, code2000; font-size: 120%;"><i>x</i><sup><i>n</i></sup> = 1</span>. Высветлілася, што яна вырашальная толькі тады, калі лік <span style="white-space: nowrap; font-family: times, serif, palatino linotype, new athena unicode, athena, gentium, code2000; font-size: 120%;"><i>n</i></span> ёсць <a href="/w/index.php?title=%D0%9F%D1%80%D0%BE%D1%81%D1%82%D1%8B_%D0%BB%D1%96%D0%BA_%D0%A4%D0%B5%D1%80%D0%BC%D0%B0&action=edit&redlink=1" class="new" title="Просты лік Ферма (няма такой старонкі)">просты лік Ферма</a> ці здабытак некалькіх розных простых лікаў Ферма. Тым самым малады студэнт, а Гаусу на той час было ўсяго дзевятнаццаць гадоў, рашыў задачу, якой беспаспяхова займаліся навукоўцы больш чым два тысячагоддзі. </p> <div class="mw-heading mw-heading2"><h2 id="Лінейная_алгебра"><span id=".D0.9B.D1.96.D0.BD.D0.B5.D0.B9.D0.BD.D0.B0.D1.8F_.D0.B0.D0.BB.D0.B3.D0.B5.D0.B1.D1.80.D0.B0"></span>Лінейная алгебра</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0&veaction=edit&section=6" title="Правіць раздзел: Лінейная алгебра" class="mw-editsection-visualeditor"><span>правіць</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0&action=edit&section=6" title="Правіць зыходнік раздзела: Лінейная алгебра"><span>правіць зыходнік</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="hatnote navigation-not-searchable">Асноўны артыкул: <b><a href="/wiki/%D0%9B%D1%96%D0%BD%D0%B5%D0%B9%D0%BD%D0%B0%D1%8F_%D0%B0%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0" title="Лінейная алгебра">Лінейная алгебра</a></b></div> <p>Лінейная алгебра — частка алгебры, якая вывучае вектары, вектарныя, або лінейныя прасторы, лінейныя адлюстравання і сістэмы лінейных ураўненняў. Да лінейнай алгебры таксама адносяць тэорыю вызначальнікаў, тэорыю матрыц, тэорыю форм (напрыклад, квадратычных), тэорыю інварыянтаў (часткова), тэнзарнае злічэнне (часткова)<sup id="cite_ref-BSE_LAlgebra_1-0" class="reference"><a href="#cite_note-BSE_LAlgebra-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup>. Сучасная лінейная алгебра робіць акцэнт на вывучэнні вектарных прастор<sup id="cite_ref-MathEnc_LAlgebra_2-0" class="reference"><a href="#cite_note-MathEnc_LAlgebra-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup>. </p><p>Лінейная, або вектарная прастора <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V(F)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> <mo stretchy="false">(</mo> <mi>F</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V(F)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/73f84e15a2d12bd6b42de5b76e3084dc0f4aa66a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.337ex; height:2.843ex;" alt="{\displaystyle V(F)}"></span> над <a href="/wiki/%D0%9F%D0%BE%D0%BB%D0%B5_(%D0%B0%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0)" title="Поле (алгебра)">полем</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/545fd099af8541605f7ee55f08225526be88ce57" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.741ex; height:2.176ex;" alt="{\displaystyle F}"></span> — гэта ўпарадкаваная чацвёрка <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (V,F,+,\cdot )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>V</mi> <mo>,</mo> <mi>F</mi> <mo>,</mo> <mo>+</mo> <mo>,</mo> <mo>⋅</mo> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (V,F,+,\cdot )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/70d66ee1401f52ea84fc39812b7b576ae1db852d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:10.894ex; height:2.843ex;" alt="{\displaystyle (V,F,+,\cdot )}"></span>, дзе </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/af0f6064540e84211d0ffe4dac72098adfa52845" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.787ex; height:2.176ex;" alt="{\displaystyle V}"></span> — непустое мноства элементаў адвольнай прыроды, якія называюцца вектарамі;</dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/545fd099af8541605f7ee55f08225526be88ce57" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.741ex; height:2.176ex;" alt="{\displaystyle F}"></span> — (алгебраічнае) поле, элементы якога называюцца скалярамі;</dd> <dd>+: V+V → V — аперацыя складання вектараў, якая супастаўляе кожнай пары элементаў <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {x} ,\mathbf {y} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">x</mi> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">y</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {x} ,\mathbf {y} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d28811e17dfee391210c4475aa6706627e72e1f4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.856ex; height:2.009ex;" alt="{\displaystyle \mathbf {x} ,\mathbf {y} }"></span> мноства <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/af0f6064540e84211d0ffe4dac72098adfa52845" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.787ex; height:2.176ex;" alt="{\displaystyle V}"></span> адзіны элемент мноства <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/af0f6064540e84211d0ffe4dac72098adfa52845" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.787ex; height:2.176ex;" alt="{\displaystyle V}"></span>, які абазначаецца <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {x} +\mathbf {y} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">x</mi> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">y</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {x} +\mathbf {y} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/489fe3f87c1bac975b1bdea1a3e7b0369d8f7a08" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:5.662ex; height:2.343ex;" alt="{\displaystyle \mathbf {x} +\mathbf {y} }"></span>;</dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \cdot \colon F\times V\to V}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>⋅</mo> <mo>:</mo> <mi>F</mi> <mo>×</mo> <mi>V</mi> <mo stretchy="false">→</mo> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \cdot \colon F\times V\to V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/14e7aab1102d928e935fbafb0f118fee474dc6de" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:13.451ex; height:2.176ex;" alt="{\displaystyle \cdot \colon F\times V\to V}"></span> — аперацыя множання вектараў на скаляры, якая супастаўляе кожнаму элементу <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lambda \in F}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>λ</mi> <mo>∈</mo> <mi>F</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lambda \in F}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/18a3dc38b2358165949ba3b1a6a1c8f0cba55aa1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.937ex; height:2.176ex;" alt="{\displaystyle \lambda \in F}"></span> і кожнаму элементу <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {x} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">x</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {x} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/32adf004df5eb0a8c7fd8c0b6b7405183c5a5ef2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.411ex; height:1.676ex;" alt="{\displaystyle \mathbf {x} }"></span> мноства <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/af0f6064540e84211d0ffe4dac72098adfa52845" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.787ex; height:2.176ex;" alt="{\displaystyle V}"></span> адзіны элемент мноства <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/af0f6064540e84211d0ffe4dac72098adfa52845" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.787ex; height:2.176ex;" alt="{\displaystyle V}"></span>, які абазначаецца <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lambda \mathbf {x} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">x</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lambda \mathbf {x} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5d3a3d96a4235bb7b60865a33257fa05749c4173" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.766ex; height:2.176ex;" alt="{\displaystyle \lambda \mathbf {x} }"></span>;</dd></dl> <p>прычым, зададзеныя аперацыі адпавядаюць наступным аксіёмам — аксіёмам лінейнай (вектарнай) прасторы: </p> <ol><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {x} +\mathbf {y} =\mathbf {y} +\mathbf {x} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">x</mi> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">y</mi> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">y</mi> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">x</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {x} +\mathbf {y} =\mathbf {y} +\mathbf {x} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/41d74ac3d2d4398f92edd91a6f194a73786d8bec" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:14.423ex; height:2.343ex;" alt="{\displaystyle \mathbf {x} +\mathbf {y} =\mathbf {y} +\mathbf {x} }"></span>, для любых <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {x} ,\mathbf {y} \in V}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">x</mi> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">y</mi> </mrow> <mo>∈</mo> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {x} ,\mathbf {y} \in V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d1e3bd206db950f7f724ab934aa3ad24a8e46c0c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.484ex; height:2.509ex;" alt="{\displaystyle \mathbf {x} ,\mathbf {y} \in V}"></span> (камутатыўнасць складання);</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {x} +(\mathbf {y} +\mathbf {z} )=(\mathbf {x} +\mathbf {y} )+\mathbf {z} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">x</mi> </mrow> <mo>+</mo> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">y</mi> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">z</mi> </mrow> <mo stretchy="false">)</mo> <mo>=</mo> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">x</mi> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">y</mi> </mrow> <mo stretchy="false">)</mo> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">z</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {x} +(\mathbf {y} +\mathbf {z} )=(\mathbf {x} +\mathbf {y} )+\mathbf {z} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/356b318f8dd1f0b0557ac5e1538594c89ceace29" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:26.099ex; height:2.843ex;" alt="{\displaystyle \mathbf {x} +(\mathbf {y} +\mathbf {z} )=(\mathbf {x} +\mathbf {y} )+\mathbf {z} }"></span>, для любых <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {x} ,\mathbf {y} ,\mathbf {z} \in V}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">x</mi> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">y</mi> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">z</mi> </mrow> <mo>∈</mo> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {x} ,\mathbf {y} ,\mathbf {z} \in V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b911b1a1eaf6f0e455f8c6aa2c8336a71a707dcb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:10.706ex; height:2.509ex;" alt="{\displaystyle \mathbf {x} ,\mathbf {y} ,\mathbf {z} \in V}"></span> (асацыятыўнасць складання);</li> <li>існуе такі элемент <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \theta \in V}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>θ</mi> <mo>∈</mo> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \theta \in V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1009a0e43b1fe266deac07f2298853dbe0ce8b4f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.718ex; height:2.176ex;" alt="{\displaystyle \theta \in V}"></span>, што <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {x} +\theta =\mathbf {x} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">x</mi> </mrow> <mo>+</mo> <mi>θ</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">x</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {x} +\theta =\mathbf {x} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b7485bab2bace8c08767dc4ada4c7fa243ea8745" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:9.851ex; height:2.343ex;" alt="{\displaystyle \mathbf {x} +\theta =\mathbf {x} }"></span> для любога <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {x} \in V}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">x</mi> </mrow> <mo>∈</mo> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {x} \in V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6fa73d235288055c446c5cec944804b0cfda4962" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.039ex; height:2.176ex;" alt="{\displaystyle \mathbf {x} \in V}"></span> (існаванне нейтральнага элемента адносна складання), у прыватнасці <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/af0f6064540e84211d0ffe4dac72098adfa52845" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.787ex; height:2.176ex;" alt="{\displaystyle V}"></span> не пуста;</li> <li>для любога <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {x} \in V}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">x</mi> </mrow> <mo>∈</mo> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {x} \in V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6fa73d235288055c446c5cec944804b0cfda4962" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.039ex; height:2.176ex;" alt="{\displaystyle \mathbf {x} \in V}"></span> існуе такі элемент <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle -\mathbf {x} \in V}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">x</mi> </mrow> <mo>∈</mo> <mi>V</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle -\mathbf {x} \in V}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f2d8258dbea45ca00a6ee94d7ac2d8d5acf0a5f2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:7.847ex; height:2.343ex;" alt="{\displaystyle -\mathbf {x} \in V}"></span>, што <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {x} +(-\mathbf {x} )=\theta }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">x</mi> </mrow> <mo>+</mo> <mo stretchy="false">(</mo> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">x</mi> </mrow> <mo stretchy="false">)</mo> <mo>=</mo> <mi>θ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {x} +(-\mathbf {x} )=\theta }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0f7643a3a728601afc9c55a4fe430301cea57809" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.469ex; height:2.843ex;" alt="{\displaystyle \mathbf {x} +(-\mathbf {x} )=\theta }"></span> (існаванне супрацьлеглага элемента адносна складання).</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha (\beta \mathbf {x} )=(\alpha \beta )\mathbf {x} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>α</mi> <mo stretchy="false">(</mo> <mi>β</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">x</mi> </mrow> <mo stretchy="false">)</mo> <mo>=</mo> <mo stretchy="false">(</mo> <mi>α</mi> <mi>β</mi> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">x</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha (\beta \mathbf {x} )=(\alpha \beta )\mathbf {x} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cf0f091a36b7bfc71bf1f0120f88c7ac4d0b9f06" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:15.178ex; height:2.843ex;" alt="{\displaystyle \alpha (\beta \mathbf {x} )=(\alpha \beta )\mathbf {x} }"></span> (асацыятыўнасць множання на скаляр);</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 1\cdot \mathbf {x} =\mathbf {x} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1</mn> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">x</mi> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">x</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1\cdot \mathbf {x} =\mathbf {x} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9dd2078f25d59846b4db7f6f9f32a2d7f7750514" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:8.762ex; height:2.176ex;" alt="{\displaystyle 1\cdot \mathbf {x} =\mathbf {x} }"></span> (унітарнае: множанне на нейтральны (па множанню) элемент поля F захоўвае вектар).</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (\alpha +\beta )\mathbf {x} =\alpha \mathbf {x} +\beta \mathbf {x} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>α</mi> <mo>+</mo> <mi>β</mi> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">x</mi> </mrow> <mo>=</mo> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">x</mi> </mrow> <mo>+</mo> <mi>β</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">x</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (\alpha +\beta )\mathbf {x} =\alpha \mathbf {x} +\beta \mathbf {x} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/729df05a7e642aa88ddd0fc6427fcffd7c110f7a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:20.461ex; height:2.843ex;" alt="{\displaystyle (\alpha +\beta )\mathbf {x} =\alpha \mathbf {x} +\beta \mathbf {x} }"></span> (дыстрыбутыўнасць множання на вектар адносна складання скаляраў);</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha (\mathbf {x} +\mathbf {y} )=\alpha \mathbf {x} +\alpha \mathbf {y} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>α</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">x</mi> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">y</mi> </mrow> <mo stretchy="false">)</mo> <mo>=</mo> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">x</mi> </mrow> <mo>+</mo> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">y</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha (\mathbf {x} +\mathbf {y} )=\alpha \mathbf {x} +\alpha \mathbf {y} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/67c30fba76f4a69e5a0e9b5c70433b7bde5e1c84" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:20.695ex; height:2.843ex;" alt="{\displaystyle \alpha (\mathbf {x} +\mathbf {y} )=\alpha \mathbf {x} +\alpha \mathbf {y} }"></span> (дыстрыбутыўнасць множання на скаляр адносна складання вектараў).</li></ol> <p>Эўклідавыя прасторы, афінныя прасторы, а таксама многія іншыя прасторы, якія вывучаюцца ў геаметрыі, вызначаюцца на аснове вектарнай прасторы. Аўтамарфізмы вектарнай прасторы над полем ўтвараюць групу адносна множання, ізаморфную групе нявыраджаных квадратных матрыц, што звязвае лінейную алгебру з тэорыяй груп, у прыватнасці з тэорыяй лінейных прадстаўленняў груп<sup id="cite_ref-MathEnc_LAlgebra_2-1" class="reference"><a href="#cite_note-MathEnc_LAlgebra-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup>. </p><p>Пераход ад канечнамерных вектарных прастор, якія звычайна выкарыстоўваюцца ў лінейнай алгебры, да бесканечнамерных лінейных прастор знайшоў сваё адлюстраванне ў некаторых раздзелах функцыянальнага аналізу<sup id="cite_ref-BSE_LAlgebra_1-1" class="reference"><a href="#cite_note-BSE_LAlgebra-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup>. Іншым натуральным абагульненнем з’яўляецца выкарыстанне не поля, а адвольнага кольца. Для модуля над адвольным кальцом не выконваюцца асноўныя тэарэмы лінейнай алгебры. Агульныя ўласцівасці вектарных прастор над полем і модуляў над кальцом вывучаюцца ў алгебраічнай К-тэорыі<sup id="cite_ref-MathEnc_LAlgebra_2-2" class="reference"><a href="#cite_note-MathEnc_LAlgebra-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup>. </p> <div class="mw-heading mw-heading2"><h2 id="Агульная_алгебра"><span id=".D0.90.D0.B3.D1.83.D0.BB.D1.8C.D0.BD.D0.B0.D1.8F_.D0.B0.D0.BB.D0.B3.D0.B5.D0.B1.D1.80.D0.B0"></span>Агульная алгебра</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0&veaction=edit&section=7" title="Правіць раздзел: Агульная алгебра" class="mw-editsection-visualeditor"><span>правіць</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0&action=edit&section=7" title="Правіць зыходнік раздзела: Агульная алгебра"><span>правіць зыходнік</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="hatnote navigation-not-searchable">Асноўны артыкул: <b><a href="/wiki/%D0%90%D0%B3%D1%83%D0%BB%D1%8C%D0%BD%D0%B0%D1%8F_%D0%B0%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0" class="mw-redirect" title="Агульная алгебра">Агульная алгебра</a></b></div> <p>Агульная алгебра займаецца вывучэннем розных алгебраічных сістэм. У ёй разглядаюцца ўласцівасці аперацый над аб’ектамі незалежна ад уласна прыроды аб’ектаў<sup id="cite_ref-BSE_Algebra_3-0" class="reference"><a href="#cite_note-BSE_Algebra-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup>. Яна ўключае ў сябе ў першую чаргу тэорыі груп і кольцаў. Агульныя ўласцівасці, характэрныя для абодвух відаў алгебраічных сістэм прывялі да разгляду новых алгебраічных сістэм: рашотак, катэгорый, універсальных алгебр, мадэлей, паўгруп і квазігруп. Упарадкаваныя і тапалагічныя алгебры, часткова ўпарадкаваныя і тапалагічныя групы і кольцы, таксама адносяцца да агульнай алгебры<sup id="cite_ref-MathEnc_AAlgebra_4-0" class="reference"><a href="#cite_note-MathEnc_AAlgebra-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup>. </p><p>Дакладная мяжа агульнай алгебры не вызначана. Да яе можна таксама аднесці тэорыю палёў, канечных груп, канечнамерныя алгебры Лі<sup id="cite_ref-MathEnc_AAlgebra_4-1" class="reference"><a href="#cite_note-MathEnc_AAlgebra-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup>. </p> <div class="mw-heading mw-heading3"><h3 id="Тэорыя_груп"><span id=".D0.A2.D1.8D.D0.BE.D1.80.D1.8B.D1.8F_.D0.B3.D1.80.D1.83.D0.BF"></span>Тэорыя груп</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0&veaction=edit&section=8" title="Правіць раздзел: Тэорыя груп" class="mw-editsection-visualeditor"><span>правіць</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0&action=edit&section=8" title="Правіць зыходнік раздзела: Тэорыя груп"><span>правіць зыходнік</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="hatnote navigation-not-searchable">Асноўны артыкул: <b><a href="/wiki/%D0%A2%D1%8D%D0%BE%D1%80%D1%8B%D1%8F_%D0%B3%D1%80%D1%83%D0%BF" title="Тэорыя груп">Тэорыя груп</a></b></div> <p>Непустое мноства <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle G}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>G</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle G}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f5f3c8921a3b352de45446a6789b104458c9f90b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.827ex; height:2.176ex;" alt="{\displaystyle G}"></span> з зададзенай на ім бінарнай аперацыяй <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \,*\,\colon G\times G\to G}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="thinmathspace" /> <mo>∗</mo> <mspace width="thinmathspace" /> <mo>:</mo> <mi>G</mi> <mo>×</mo> <mi>G</mi> <mo stretchy="false">→</mo> <mi>G</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \,*\,\colon G\times G\to G}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cefe97616869a2c844d8860711b0ee71a0dd7d52" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:14.905ex; height:2.176ex;" alt="{\displaystyle \,*\,\colon G\times G\to G}"></span> называецца групай <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (G,*)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>G</mi> <mo>,</mo> <mo>∗</mo> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (G,*)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e54a87abf331634c8962ef14c4c5ec41f94fd29c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.832ex; height:2.843ex;" alt="{\displaystyle (G,*)}"></span>, калі выкананы наступныя аксіёмы: </p> <ul><li>асацыятыўнасць: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \forall (a,b,c\in G):(a*b)*c=a*(b*c)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∀</mi> <mo stretchy="false">(</mo> <mi>a</mi> <mo>,</mo> <mi>b</mi> <mo>,</mo> <mi>c</mi> <mo>∈</mo> <mi>G</mi> <mo stretchy="false">)</mo> <mo>:</mo> <mo stretchy="false">(</mo> <mi>a</mi> <mo>∗</mo> <mi>b</mi> <mo stretchy="false">)</mo> <mo>∗</mo> <mi>c</mi> <mo>=</mo> <mi>a</mi> <mo>∗</mo> <mo stretchy="false">(</mo> <mi>b</mi> <mo>∗</mo> <mi>c</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \forall (a,b,c\in G):(a*b)*c=a*(b*c)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8812641d4bf1963b9db242a437ef1b4324ff0470" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:36.973ex; height:2.843ex;" alt="{\displaystyle \forall (a,b,c\in G):(a*b)*c=a*(b*c)}"></span>;</li> <li>наяўнасць нейтральнага элемента: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \exists e\in G\quad \forall a\in G:(e*a=a*e=a)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∃</mi> <mi>e</mi> <mo>∈</mo> <mi>G</mi> <mspace width="1em" /> <mi mathvariant="normal">∀</mi> <mi>a</mi> <mo>∈</mo> <mi>G</mi> <mo>:</mo> <mo stretchy="false">(</mo> <mi>e</mi> <mo>∗</mo> <mi>a</mi> <mo>=</mo> <mi>a</mi> <mo>∗</mo> <mi>e</mi> <mo>=</mo> <mi>a</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \exists e\in G\quad \forall a\in G:(e*a=a*e=a)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/09be93c6a9eb508ed6aa38eb47ecf94f92aaf95b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:36.745ex; height:2.843ex;" alt="{\displaystyle \exists e\in G\quad \forall a\in G:(e*a=a*e=a)}"></span>;</li> <li>наяўнасць адваротнага элемента: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \forall a\in G\quad \exists a^{-1}\in G:(a*a^{-1}=a^{-1}*a=e)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∀</mi> <mi>a</mi> <mo>∈</mo> <mi>G</mi> <mspace width="1em" /> <mi mathvariant="normal">∃</mi> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mo>∈</mo> <mi>G</mi> <mo>:</mo> <mo stretchy="false">(</mo> <mi>a</mi> <mo>∗</mo> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mo>=</mo> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mo>∗</mo> <mi>a</mi> <mo>=</mo> <mi>e</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \forall a\in G\quad \exists a^{-1}\in G:(a*a^{-1}=a^{-1}*a=e)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/58a523d28adfd246975513d1dacaee3e5c2769dc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:44.036ex; height:3.176ex;" alt="{\displaystyle \forall a\in G\quad \exists a^{-1}\in G:(a*a^{-1}=a^{-1}*a=e)}"></span></li></ul> <p>Паняцце групы ўзнікла ў выніку фармальнага апісання сіметрыі і эквівалентнасці геаметрычных аб’ектаў. У тэорыі Галуа, якая і дала пачатак паняццю групы, групы выкарыстоўваюцца для апісання сіметрыі ўраўненняў, каранямі якіх з’яўляюцца карані некаторага паліномнага ўраўнення. Групы паўсюдна выкарыстоўваюцца ў матэматыцы і прыродазнаўчых навуках, часта для выяўлення ўнутранай сіметрыі аб’ектаў (групы аўтамарфізмаў). Амаль усе структуры агульнай алгебры — асобныя выпадкі груп. </p> <div class="mw-heading mw-heading3"><h3 id="Тэорыя_кольцаў"><span id=".D0.A2.D1.8D.D0.BE.D1.80.D1.8B.D1.8F_.D0.BA.D0.BE.D0.BB.D1.8C.D1.86.D0.B0.D1.9E"></span>Тэорыя кольцаў</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0&veaction=edit&section=9" title="Правіць раздзел: Тэорыя кольцаў" class="mw-editsection-visualeditor"><span>правіць</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0&action=edit&section=9" title="Правіць зыходнік раздзела: Тэорыя кольцаў"><span>правіць зыходнік</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Кальцо — гэта мноства R, на якім зададзены дзве бінарныя аперацыі: + і × (так званыя складанне і множанне), з наступнымі ўласцівасцямі: </p> <ol><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \forall a,b\in R\left(a+b=b+a\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∀</mi> <mi>a</mi> <mo>,</mo> <mi>b</mi> <mo>∈</mo> <mi>R</mi> <mrow> <mo>(</mo> <mrow> <mi>a</mi> <mo>+</mo> <mi>b</mi> <mo>=</mo> <mi>b</mi> <mo>+</mo> <mi>a</mi> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \forall a,b\in R\left(a+b=b+a\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b74f1982247d04f5cdf99fcd938ad9d82a6e14e5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:24.589ex; height:2.843ex;" alt="{\displaystyle \forall a,b\in R\left(a+b=b+a\right)}"></span> — камутатыўнасць складання;</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \forall a,b,c\in R\left(a+(b+c))=((a+b)+c\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∀</mi> <mi>a</mi> <mo>,</mo> <mi>b</mi> <mo>,</mo> <mi>c</mi> <mo>∈</mo> <mi>R</mi> <mrow> <mo>(</mo> <mrow> <mi>a</mi> <mo>+</mo> <mo stretchy="false">(</mo> <mi>b</mi> <mo>+</mo> <mi>c</mi> <mo stretchy="false">)</mo> <mo stretchy="false">)</mo> <mo>=</mo> <mo stretchy="false">(</mo> <mo stretchy="false">(</mo> <mi>a</mi> <mo>+</mo> <mi>b</mi> <mo stretchy="false">)</mo> <mo>+</mo> <mi>c</mi> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \forall a,b,c\in R\left(a+(b+c))=((a+b)+c\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ddc26721fc0f420cd6d5096b5db52ef7431f124c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:39.752ex; height:2.843ex;" alt="{\displaystyle \forall a,b,c\in R\left(a+(b+c))=((a+b)+c\right)}"></span> — асацыятыўнасць складання;</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \exists 0\in R\;\forall a\in R\left(a+0=0+a=a\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∃</mi> <mn>0</mn> <mo>∈</mo> <mi>R</mi> <mspace width="thickmathspace" /> <mi mathvariant="normal">∀</mi> <mi>a</mi> <mo>∈</mo> <mi>R</mi> <mrow> <mo>(</mo> <mrow> <mi>a</mi> <mo>+</mo> <mn>0</mn> <mo>=</mo> <mn>0</mn> <mo>+</mo> <mi>a</mi> <mo>=</mo> <mi>a</mi> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \exists 0\in R\;\forall a\in R\left(a+0=0+a=a\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/aaf7e2c3eaf5f2e18ec6f461972b199b973b7f12" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:34.92ex; height:2.843ex;" alt="{\displaystyle \exists 0\in R\;\forall a\in R\left(a+0=0+a=a\right)}"></span> — існаванне нейтральнага элемента адносна складання;</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \forall a\in R\;\exists b\in R\left(a+b=b+a=0\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∀</mi> <mi>a</mi> <mo>∈</mo> <mi>R</mi> <mspace width="thickmathspace" /> <mi mathvariant="normal">∃</mi> <mi>b</mi> <mo>∈</mo> <mi>R</mi> <mrow> <mo>(</mo> <mrow> <mi>a</mi> <mo>+</mo> <mi>b</mi> <mo>=</mo> <mi>b</mi> <mo>+</mo> <mi>a</mi> <mo>=</mo> <mn>0</mn> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \forall a\in R\;\exists b\in R\left(a+b=b+a=0\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1d07888c86657ac3e0c139bc064058322848c30b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:34.358ex; height:2.843ex;" alt="{\displaystyle \forall a\in R\;\exists b\in R\left(a+b=b+a=0\right)}"></span> — існаванне супрацьлеглага элемента адносна складання;</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \forall a,b,c\in R\;(a\times b)\times c=a\times (b\times c)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∀</mi> <mi>a</mi> <mo>,</mo> <mi>b</mi> <mo>,</mo> <mi>c</mi> <mo>∈</mo> <mi>R</mi> <mspace width="thickmathspace" /> <mo stretchy="false">(</mo> <mi>a</mi> <mo>×</mo> <mi>b</mi> <mo stretchy="false">)</mo> <mo>×</mo> <mi>c</mi> <mo>=</mo> <mi>a</mi> <mo>×</mo> <mo stretchy="false">(</mo> <mi>b</mi> <mo>×</mo> <mi>c</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \forall a,b,c\in R\;(a\times b)\times c=a\times (b\times c)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d6c42b4aa2d8f7744aeedb6eb44795377bd313b2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:36.391ex; height:2.843ex;" alt="{\displaystyle \forall a,b,c\in R\;(a\times b)\times c=a\times (b\times c)}"></span> — асацыятыўнасць множання (некаторыя аўтары не патрабуюць выканання гэтай аксіёмы)</li> <li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \forall a,b,c\in R\left\{{\begin{matrix}a\times (b+c)=a\times b+a\times c\\(b+c)\times a=b\times a+c\times a\end{matrix}}\right.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∀</mi> <mi>a</mi> <mo>,</mo> <mi>b</mi> <mo>,</mo> <mi>c</mi> <mo>∈</mo> <mi>R</mi> <mrow> <mo>{</mo> <mrow class="MJX-TeXAtom-ORD"> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mi>a</mi> <mo>×</mo> <mo stretchy="false">(</mo> <mi>b</mi> <mo>+</mo> <mi>c</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>a</mi> <mo>×</mo> <mi>b</mi> <mo>+</mo> <mi>a</mi> <mo>×</mo> <mi>c</mi> </mtd> </mtr> <mtr> <mtd> <mo stretchy="false">(</mo> <mi>b</mi> <mo>+</mo> <mi>c</mi> <mo stretchy="false">)</mo> <mo>×</mo> <mi>a</mi> <mo>=</mo> <mi>b</mi> <mo>×</mo> <mi>a</mi> <mo>+</mo> <mi>c</mi> <mo>×</mo> <mi>a</mi> </mtd> </mtr> </mtable> </mrow> <mo fence="true" stretchy="true" symmetric="true"></mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \forall a,b,c\in R\left\{{\begin{matrix}a\times (b+c)=a\times b+a\times c\\(b+c)\times a=b\times a+c\times a\end{matrix}}\right.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/be77d718e901b10f95f4f510eaacbdd0c5f90213" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:40.889ex; height:6.176ex;" alt="{\displaystyle \forall a,b,c\in R\left\{{\begin{matrix}a\times (b+c)=a\times b+a\times c\\(b+c)\times a=b\times a+c\times a\end{matrix}}\right.}"></span> — дыстрыбутыўнасць.</li></ol> <div class="mw-heading mw-heading2"><h2 id="Універсальная_алгебра"><span id=".D0.A3.D0.BD.D1.96.D0.B2.D0.B5.D1.80.D1.81.D0.B0.D0.BB.D1.8C.D0.BD.D0.B0.D1.8F_.D0.B0.D0.BB.D0.B3.D0.B5.D0.B1.D1.80.D0.B0"></span>Універсальная алгебра</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0&veaction=edit&section=10" title="Правіць раздзел: Універсальная алгебра" class="mw-editsection-visualeditor"><span>правіць</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0&action=edit&section=10" title="Правіць зыходнік раздзела: Універсальная алгебра"><span>правіць зыходнік</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="hatnote navigation-not-searchable">Асноўны артыкул: <b><a href="/w/index.php?title=%D0%A3%D0%BD%D1%96%D0%B2%D0%B5%D1%80%D1%81%D0%B0%D0%BB%D1%8C%D0%BD%D0%B0%D1%8F_%D0%B0%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0&action=edit&redlink=1" class="new" title="Універсальная алгебра (няма такой старонкі)">Універсальная алгебра</a></b></div> <p>Універсальная алгебра з’яўляецца спецыяльным раздзелам агульнай алгебры, які займаецца вывучэннем характэрных для ўсіх алгебраічных сістэм уласцівасцей. Алгебраічная сістэма ўяўляе сабой адвольнае непустое мноства з зададзеным (магчыма, бесканечным) наборам канечнаарных аперацый над ім і канечнаарных адносін: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathfrak {A}}=\langle A,F,R\rangle }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="fraktur">A</mi> </mrow> </mrow> <mo>=</mo> <mo fence="false" stretchy="false">⟨</mo> <mi>A</mi> <mo>,</mo> <mi>F</mi> <mo>,</mo> <mi>R</mi> <mo fence="false" stretchy="false">⟩</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathfrak {A}}=\langle A,F,R\rangle }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/036e5e784c6c527fb03d133582c9f71a7478585c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.892ex; height:2.843ex;" alt="{\displaystyle {\mathfrak {A}}=\langle A,F,R\rangle }"></span>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle F=\langle f_{1}:A^{n_{1}}\to A,\dots f_{i}:A^{n_{i}}\to A,\dots \rangle }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>F</mi> <mo>=</mo> <mo fence="false" stretchy="false">⟨</mo> <msub> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>:</mo> <msup> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> </msup> <mo stretchy="false">→</mo> <mi>A</mi> <mo>,</mo> <mo>…</mo> <msub> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>:</mo> <msup> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mrow> </msup> <mo stretchy="false">→</mo> <mi>A</mi> <mo>,</mo> <mo>…</mo> <mo fence="false" stretchy="false">⟩</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle F=\langle f_{1}:A^{n_{1}}\to A,\dots f_{i}:A^{n_{i}}\to A,\dots \rangle }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/13f1de08c75ccbc315f86cb79b0f65ca68f13628" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:40.651ex; height:2.843ex;" alt="{\displaystyle F=\langle f_{1}:A^{n_{1}}\to A,\dots f_{i}:A^{n_{i}}\to A,\dots \rangle }"></span>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R=\langle r_{1}\subseteq A^{m_{1}},\dots r_{i}\subseteq A^{m_{i}},\dots \rangle }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>R</mi> <mo>=</mo> <mo fence="false" stretchy="false">⟨</mo> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>⊆</mo> <msup> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> </msup> <mo>,</mo> <mo>…</mo> <msub> <mi>r</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>⊆</mo> <msup> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mrow> </msup> <mo>,</mo> <mo>…</mo> <mo fence="false" stretchy="false">⟩</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle R=\langle r_{1}\subseteq A^{m_{1}},\dots r_{i}\subseteq A^{m_{i}},\dots \rangle }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/aa51e8fb4ce07d08a5d117884a36c40692ed480f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:33.014ex; height:2.843ex;" alt="{\displaystyle R=\langle r_{1}\subseteq A^{m_{1}},\dots r_{i}\subseteq A^{m_{i}},\dots \rangle }"></span>. Мноства <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7daff47fa58cdfd29dc333def748ff5fa4c923e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}"></span> ў гэтым выпадку называецца носьбітам (або асноўным мноствам) сістэмы, набор функцыянальных і прэдыкатных знакаў з іх арнасцямі <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \langle F,R,\langle n_{1},\dots n_{i},\dots \rangle ,\langle m_{1}\dots m_{i},\dots \rangle \rangle }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo fence="false" stretchy="false">⟨</mo> <mi>F</mi> <mo>,</mo> <mi>R</mi> <mo>,</mo> <mo fence="false" stretchy="false">⟨</mo> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <mo>…</mo> <msub> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>,</mo> <mo>…</mo> <mo fence="false" stretchy="false">⟩</mo> <mo>,</mo> <mo fence="false" stretchy="false">⟨</mo> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>…</mo> <msub> <mi>m</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>,</mo> <mo>…</mo> <mo fence="false" stretchy="false">⟩</mo> <mo fence="false" stretchy="false">⟩</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \langle F,R,\langle n_{1},\dots n_{i},\dots \rangle ,\langle m_{1}\dots m_{i},\dots \rangle \rangle }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9e78a97b199c1fd133207f9fc52f8adfb6834f9b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:37.769ex; height:2.843ex;" alt="{\displaystyle \langle F,R,\langle n_{1},\dots n_{i},\dots \rangle ,\langle m_{1}\dots m_{i},\dots \rangle \rangle }"></span> — яе сігнатурай. Сістэма з пустым мноствам адносін называецца ўніверсальнай алгебрай (у кантэксце прадмета — часцей проста алгебрай), а з пустым мноствам аперацый — мадэллю або сістэмай адносін, рэляцыйнай сістэмай. </p><p>У тэрмінах універсальнай алгебры, напрыклад, кальцо — гэта універсальная алгебра <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left(R,+,\times \right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>(</mo> <mrow> <mi>R</mi> <mo>,</mo> <mo>+</mo> <mo>,</mo> <mo>×</mo> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left(R,+,\times \right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9e948dfce36abbb75b3dbf92e29e0da64b1f41fb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.257ex; height:2.843ex;" alt="{\displaystyle \left(R,+,\times \right)}"></span>, такая што алгебра <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left(R,+\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>(</mo> <mrow> <mi>R</mi> <mo>,</mo> <mo>+</mo> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left(R,+\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a76f48a86a489e5f1a825837c2bedc5ec88c62d4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.415ex; height:2.843ex;" alt="{\displaystyle \left(R,+\right)}"></span> — абелева група, і аперацыя <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle +}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>+</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle +}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fe6ef363cd19902d1a7a71fb1c8b21e8ede52406" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:1.808ex; height:2.176ex;" alt="{\displaystyle +}"></span> дыстрыбутыўная злева і справа адносна <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \times }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>×</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \times }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0ffafff1ad26cbe49045f19a67ce532116a32703" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: 0.019ex; margin-bottom: -0.19ex; width:1.808ex; height:1.509ex;" alt="{\displaystyle \times }"></span>. Кальцо называецца асацыятыўным, калі мультыплікатыўны групоід з’яўляецца паўгрупай. Раздзел разглядае як уласна ўніверсальныя алгебры, так і спадарожныя структуры: маноід ўсіх эндамарфізмаў <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {End} {\mathfrak {A}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">E</mi> <mi mathvariant="bold">n</mi> <mi mathvariant="bold">d</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="fraktur">A</mi> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {End} {\mathfrak {A}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e5906d522c92ed5ce867c576dba9a3f6d2fdbf11" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.396ex; height:2.176ex;" alt="{\displaystyle \mathbf {End} {\mathfrak {A}}}"></span>, група усіх аўтамарфізмаў <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {Aut} {\mathfrak {A}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">A</mi> <mi mathvariant="bold">u</mi> <mi mathvariant="bold">t</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="fraktur">A</mi> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {Aut} {\mathfrak {A}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/efcecd4f80e2c3c5d4f4a0d7ec9e15e4c5e39e7f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.213ex; height:2.176ex;" alt="{\displaystyle \mathbf {Aut} {\mathfrak {A}}}"></span>, рашотак усіх падалгебр <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {Sub} {\mathfrak {A}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">S</mi> <mi mathvariant="bold">u</mi> <mi mathvariant="bold">b</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="fraktur">A</mi> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {Sub} {\mathfrak {A}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9be9e70e5659768247e556fa65050b31f8a9ebd6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.125ex; height:2.176ex;" alt="{\displaystyle \mathbf {Sub} {\mathfrak {A}}}"></span> і ўсіх кангруэнцый <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbf {Con} {\mathfrak {A}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="bold">C</mi> <mi mathvariant="bold">o</mi> <mi mathvariant="bold">n</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="fraktur">A</mi> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbf {Con} {\mathfrak {A}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f67ef8bdeb68c64f99a6b3ffbf53f97c60a5d866" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.422ex; height:2.176ex;" alt="{\displaystyle \mathbf {Con} {\mathfrak {A}}}"></span><sup id="cite_ref-MathEnc_UAlgebra_5-0" class="reference"><a href="#cite_note-MathEnc_UAlgebra-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup>. </p><p>Універсальная алгебра знаходзіцца на стыку логікі і алгебры<sup id="cite_ref-MathEnc_AAlgebra_4-2" class="reference"><a href="#cite_note-MathEnc_AAlgebra-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup>. </p> <div class="mw-heading mw-heading2"><h2 id="Крыніцы"><span id=".D0.9A.D1.80.D1.8B.D0.BD.D1.96.D1.86.D1.8B"></span>Крыніцы</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0&veaction=edit&section=11" title="Правіць раздзел: Крыніцы" class="mw-editsection-visualeditor"><span>правіць</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0&action=edit&section=11" title="Правіць зыходнік раздзела: Крыніцы"><span>правіць зыходнік</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="reflist columns" style="list-style-type: decimal;"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-BSE_LAlgebra-1"><span class="mw-cite-backlink">↑ <a href="#cite_ref-BSE_LAlgebra_1-0"><sup><i><b>а</b></i></sup></a> <a href="#cite_ref-BSE_LAlgebra_1-1"><sup><i><b>б</b></i></sup></a></span> <span class="reference-text"><span class="citation"><span style="" lang="und"><a rel="nofollow" class="external text" href="http://slovari.yandex.ru/линейная%20алгебра/БСЭ/Линейная%20алгебра/">Линейная алгебра</a></span><span class="hidden-ref" style="display:none"><b> <span class="ref-info" style="cursor:help;" title="нявызначанай мовай">(нявызн.)</span></b></span><span class="ref-info">(недаступная спасылка)</span>.  Большая советская энциклопедия. <small><a rel="nofollow" class="external text" href="https://web.archive.org/web/20140718090243/http://slovari.yandex.ru/%D0%BB%D0%B8%D0%BD%D0%B5%D0%B9%D0%BD%D0%B0%D1%8F%20%D0%B0%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0/%D0%91%D0%A1%D0%AD/%D0%9B%D0%B8%D0%BD%D0%B5%D0%B9%D0%BD%D0%B0%D1%8F%20%D0%B0%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0/">Архівавана</a> з першакрыніцы 18 ліпеня 2014.</small> <small>Праверана 20 снежня 2012.</small></span></span> </li> <li id="cite_note-MathEnc_LAlgebra-2"><span class="mw-cite-backlink">↑ <a href="#cite_ref-MathEnc_LAlgebra_2-0"><sup><i><b>а</b></i></sup></a> <a href="#cite_ref-MathEnc_LAlgebra_2-1"><sup><i><b>б</b></i></sup></a> <a href="#cite_ref-MathEnc_LAlgebra_2-2"><sup><i><b>в</b></i></sup></a></span> <span class="reference-text"><span class="citation no-wikidata" data-wikidata-property-id="P1343"><i>Виноградов И. М.</i> <span data-wikidata-qualifier-id="P248">Линейная алгебра</span> // <a rel="nofollow" class="external text" href="http://dic.academic.ru/dic.nsf/enc_mathematics/2759/ЛИНЕЙНАЯ">Математическая энциклопедия</a>. — <span style="border-bottom:1px dotted gray; cursor:default" title="Масква">М</span>.: Советская энциклопедия, 1977.</span></span> </li> <li id="cite_note-BSE_Algebra-3"><span class="mw-cite-backlink"><a href="#cite_ref-BSE_Algebra_3-0">↑</a></span> <span class="reference-text"><span class="citation"><span style="" lang="und"><a rel="nofollow" class="external text" href="http://slovari.yandex.ru/алгебра/БСЭ/Алгебра/">Алгебра</a></span><span class="hidden-ref" style="display:none"><b> <span class="ref-info" style="cursor:help;" title="нявызначанай мовай">(нявызн.)</span></b></span><span class="ref-info">(недаступная спасылка)</span>.  Большая советская энциклопедия. <small><a rel="nofollow" class="external text" href="https://web.archive.org/web/20140718095335/http://slovari.yandex.ru/%D0%B0%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0/%D0%91%D0%A1%D0%AD/%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0/">Архівавана</a> з першакрыніцы 18 ліпеня 2014.</small> <small>Праверана 29 снежня 2012.</small></span></span> </li> <li id="cite_note-MathEnc_AAlgebra-4"><span class="mw-cite-backlink">↑ <a href="#cite_ref-MathEnc_AAlgebra_4-0"><sup><i><b>а</b></i></sup></a> <a href="#cite_ref-MathEnc_AAlgebra_4-1"><sup><i><b>б</b></i></sup></a> <a href="#cite_ref-MathEnc_AAlgebra_4-2"><sup><i><b>в</b></i></sup></a></span> <span class="reference-text"><span class="citation no-wikidata" data-wikidata-property-id="P1343"><i>Виноградов И. М.</i> <span data-wikidata-qualifier-id="P248">Общая алгебра</span> // Математическая энциклопедия. — <span style="border-bottom:1px dotted gray; cursor:default" title="Масква">М</span>.: Советская энциклопедия, 1977.</span></span> </li> <li id="cite_note-MathEnc_UAlgebra-5"><span class="mw-cite-backlink"><a href="#cite_ref-MathEnc_UAlgebra_5-0">↑</a></span> <span class="reference-text"><span class="citation no-wikidata" data-wikidata-property-id="P1343"><i>Виноградов И. М.</i> <span data-wikidata-qualifier-id="P248">Универсальная алгебра</span> // Математическая энциклопедия. — <span style="border-bottom:1px dotted gray; cursor:default" title="Масква">М</span>.: Советская энциклопедия, 1977.</span></span> </li> </ol></div> </div> <div class="mw-heading mw-heading2"><h2 id="Спасылкі"><span id=".D0.A1.D0.BF.D0.B0.D1.81.D1.8B.D0.BB.D0.BA.D1.96"></span>Спасылкі</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0&veaction=edit&section=12" title="Правіць раздзел: Спасылкі" class="mw-editsection-visualeditor"><span>правіць</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0&action=edit&section=12" title="Правіць зыходнік раздзела: Спасылкі"><span>правіць зыходнік</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><span typeof="mw:File"><a href="/wiki/%D0%92%D1%96%D0%BA%D1%96%D1%81%D1%85%D0%BE%D0%B2%D1%96%D1%88%D1%87%D0%B0" title="Лагатып Вікісховішча"><img alt="Лагатып Вікісховішча" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/12px-Commons-logo.svg.png" decoding="async" width="12" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/18px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/24px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></a></span> На <a href="/wiki/%D0%92%D1%96%D0%BA%D1%96%D1%81%D1%85%D0%BE%D0%B2%D1%96%D1%88%D1%87%D0%B0" title="Вікісховішча">Вікісховішчы</a> ёсць медыяфайлы па тэме <a href="https://commons.wikimedia.org/wiki/Category:Algebra" class="extiw" title="commons:Category:Algebra">Алгебра</a></li></ul> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r4785216">.mw-parser-output .navbox{box-sizing:border-box;border:1px solid #a2a9b1;width:100%;clear:both;font-size:88%;text-align:center;padding:1px;margin:1em auto 0}.mw-parser-output .navbox .navbox{margin-top:0}.mw-parser-output .navbox+.navbox,.mw-parser-output .navbox+.navbox-styles+.navbox{margin-top:-1px}.mw-parser-output .navbox-inner,.mw-parser-output .navbox-subgroup{width:100%}.mw-parser-output .navbox-group,.mw-parser-output .navbox-title,.mw-parser-output .navbox-abovebelow{padding:0.25em 1em;line-height:1.5em;text-align:center}.mw-parser-output .navbox-group{white-space:nowrap;text-align:right}.mw-parser-output .navbox,.mw-parser-output .navbox-subgroup{background-color:#fdfdfd}.mw-parser-output .navbox-list{line-height:1.5em;border-color:#fdfdfd}.mw-parser-output .navbox-list-with-group{text-align:left;border-left-width:2px;border-left-style:solid}.mw-parser-output tr+tr>.navbox-abovebelow,.mw-parser-output tr+tr>.navbox-group,.mw-parser-output tr+tr>.navbox-image,.mw-parser-output tr+tr>.navbox-list{border-top:2px solid #fdfdfd}.mw-parser-output .navbox-title{background-color:#ccf}.mw-parser-output .navbox-abovebelow,.mw-parser-output .navbox-group,.mw-parser-output .navbox-subgroup .navbox-title{background-color:#ddf}.mw-parser-output .navbox-subgroup .navbox-group,.mw-parser-output .navbox-subgroup .navbox-abovebelow{background-color:#e6e6ff}.mw-parser-output .navbox-even{background-color:#f7f7f7}.mw-parser-output .navbox-odd{background-color:transparent}.mw-parser-output .navbox .hlist td dl,.mw-parser-output .navbox .hlist td ol,.mw-parser-output .navbox .hlist td ul,.mw-parser-output .navbox td.hlist dl,.mw-parser-output .navbox td.hlist ol,.mw-parser-output .navbox td.hlist ul{padding:0.125em 0}.mw-parser-output .navbox .navbar{display:block;font-size:100%}.mw-parser-output .navbox-title .navbar{float:left;text-align:left;margin-right:0.5em}body.skin--responsive .mw-parser-output .navbox-image img{max-width:none!important}</style></div><div role="navigation" class="navbox" aria-labelledby="Раздзелы_матэматыкі" data-name="Раздзелы матэматыкі" style="padding:3px"><table class="nowraplinks collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><span class="navbox-gear" style="float:left;text-align:left;width:5em;margin-right:0.5em"><span typeof="mw:File"><a href="/wiki/%D0%A8%D0%B0%D0%B1%D0%BB%D0%BE%D0%BD:%D0%A0%D0%B0%D0%B7%D0%B4%D0%B7%D0%B5%D0%BB%D1%8B_%D0%BC%D0%B0%D1%82%D1%8D%D0%BC%D0%B0%D1%82%D1%8B%D0%BA%D1%96" title="Прагляд гэтага шаблона"><img alt="⛭" src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c9/Wikipedia_interwiki_section_gear_icon.svg/14px-Wikipedia_interwiki_section_gear_icon.svg.png" decoding="async" width="14" height="14" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c9/Wikipedia_interwiki_section_gear_icon.svg/21px-Wikipedia_interwiki_section_gear_icon.svg.png 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0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><td class="navbox-list navbox-odd" style="width:100%;padding:0px"><div style="padding:0em 0.25em"></div><table class="nowraplinks collapsible collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Алгебра" style="font-size:114%;margin:0 5em"><a class="mw-selflink selflink">Алгебра</a></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd hlist hlist-items-nowrap" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%D0%AD%D0%BB%D0%B5%D0%BC%D0%B5%D0%BD%D1%82%D0%B0%D1%80%D0%BD%D0%B0%D1%8F_%D0%B0%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0" title="Элементарная алгебра">Элементарная алгебра</a></li> <li><a href="/wiki/%D0%9B%D1%96%D0%BD%D0%B5%D0%B9%D0%BD%D0%B0%D1%8F_%D0%B0%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0" title="Лінейная алгебра">Лінейная алгебра</a> <ul><li><a href="/w/index.php?title=%D0%9F%D0%BE%D0%BB%D1%96%D0%BB%D1%96%D0%BD%D0%B5%D0%B9%D0%BD%D0%B0%D1%8F_%D0%B0%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0&action=edit&redlink=1" class="new" title="Полілінейная алгебра (няма такой старонкі)">Полілінейная алгебра</a></li></ul></li> <li><a href="/wiki/%D0%90%D0%B1%D1%81%D1%82%D1%80%D0%B0%D0%BA%D1%82%D0%BD%D0%B0%D1%8F_%D0%B0%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0" title="Абстрактная алгебра">Абстрактная алгебра</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1px"><a href="/wiki/%D0%90%D0%B1%D1%81%D1%82%D1%80%D0%B0%D0%BA%D1%82%D0%BD%D0%B0%D1%8F_%D0%B0%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0" title="Абстрактная алгебра">Абстрактная алгебра</a></th><td class="navbox-list navbox-even hlist hlist-items-nowrap" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/w/index.php?title=%D0%9A%D0%B0%D0%BC%D1%83%D1%82%D0%B0%D1%82%D1%8B%D1%9E%D0%BD%D0%B0%D1%8F_%D0%B0%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0&action=edit&redlink=1" class="new" title="Камутатыўная алгебра (няма такой старонкі)">Камутатыўная алгебра</a></li> <li><a href="/wiki/%D0%A2%D1%8D%D0%BE%D1%80%D1%8B%D1%8F_%D0%BF%D1%80%D0%B0%D0%B4%D1%81%D1%82%D0%B0%D1%9E%D0%BB%D0%B5%D0%BD%D0%BD%D1%8F%D1%9E" title="Тэорыя прадстаўленняў">Тэорыя прадстаўленняў</a></li> <li><a href="/w/index.php?title=%D0%94%D1%8B%D1%84%D0%B5%D1%80%D1%8D%D0%BD%D1%86%D1%8B%D1%8F%D0%BB%D1%8C%D0%BD%D0%B0%D1%8F_%D0%B0%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0&action=edit&redlink=1" class="new" title="Дыферэнцыяльная алгебра (няма такой старонкі)">Дыферэнцыяльная алгебра</a></li> <li><a href="/w/index.php?title=%D0%93%D0%B0%D0%BC%D0%B0%D0%BB%D0%B0%D0%B3%D1%96%D1%87%D0%BD%D0%B0%D1%8F_%D0%B0%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0&action=edit&redlink=1" class="new" title="Гамалагічная алгебра (няма такой старонкі)">Гамалагічная алгебра</a></li> <li><a href="/w/index.php?title=%D0%A3%D0%BD%D1%96%D0%B2%D0%B5%D1%80%D1%81%D0%B0%D0%BB%D1%8C%D0%BD%D0%B0%D1%8F_%D0%B0%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0_(%D1%80%D0%B0%D0%B7%D0%B4%D0%B7%D0%B5%D0%BB_%D0%B0%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D1%8B)&action=edit&redlink=1" class="new" title="Універсальная алгебра (раздзел алгебры) (няма такой старонкі)">Універсальная алгебра</a></li> <li><a href="/w/index.php?title=%D0%A2%D1%8D%D0%BE%D1%80%D1%8B%D1%8F_%D0%BA%D0%B0%D1%82%D1%8D%D0%B3%D0%BE%D1%80%D1%8B%D0%B9&action=edit&redlink=1" class="new" title="Тэорыя катэгорый (няма такой старонкі)">Тэорыя катэгорый</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><td class="navbox-list navbox-odd" style="width:100%;padding:0px"><div style="padding:0em 0.25em"></div><table class="nowraplinks collapsible collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Матэматычны_аналіз" style="font-size:114%;margin:0 5em"><a href="/wiki/%D0%9C%D0%B0%D1%82%D1%8D%D0%BC%D0%B0%D1%82%D1%8B%D1%87%D0%BD%D1%8B_%D0%B0%D0%BD%D0%B0%D0%BB%D1%96%D0%B7" title="Матэматычны аналіз">Матэматычны аналіз</a></div></th></tr><tr><td class="navbox-list navbox-odd hlist hlist-items-nowrap" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%D0%92%D0%B0%D1%80%D1%8B%D1%8F%D1%86%D1%8B%D0%B9%D0%BD%D0%B0%D0%B5_%D0%B7%D0%BB%D1%96%D1%87%D1%8D%D0%BD%D0%BD%D0%B5" title="Варыяцыйнае злічэнне">Варыяцыйнае злічэнне</a></li> <li><a href="/wiki/%D0%9A%D0%B0%D0%BC%D0%BF%D0%BB%D0%B5%D0%BA%D1%81%D0%BD%D1%8B_%D0%B0%D0%BD%D0%B0%D0%BB%D1%96%D0%B7" title="Камплексны аналіз">Камплексны аналіз</a></li> <li><a href="/wiki/%D0%9C%D0%B5%D1%80%D0%B0_%D0%BC%D0%BD%D0%BE%D1%81%D1%82%D0%B2%D0%B0" title="Мера мноства">Тэорыя меры</a></li> <li><a href="/wiki/%D0%A4%D1%83%D0%BD%D0%BA%D1%86%D1%8B%D1%8F%D0%BD%D0%B0%D0%BB%D1%8C%D0%BD%D1%8B_%D0%B0%D0%BD%D0%B0%D0%BB%D1%96%D0%B7" title="Функцыянальны аналіз">Функцыянальны аналіз</a></li> <li><a href="/wiki/%D0%93%D0%B0%D1%80%D0%BC%D0%B0%D0%BD%D1%96%D1%87%D0%BD%D1%8B_%D0%B0%D0%BD%D0%B0%D0%BB%D1%96%D0%B7" title="Гарманічны аналіз">Гарманічны аналіз</a></li> <li><a href="/w/index.php?title=%D0%9D%D0%B5%D1%81%D1%82%D0%B0%D0%BD%D0%B4%D0%B0%D1%80%D1%82%D0%BD%D1%8B_%D0%B0%D0%BD%D0%B0%D0%BB%D1%96%D0%B7&action=edit&redlink=1" class="new" title="Нестандартны аналіз (няма такой старонкі)">Нестандартны аналіз</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><td class="navbox-list navbox-odd" style="width:100%;padding:0px"><div style="padding:0em 0.25em"></div><table class="nowraplinks collapsible collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Геаметрыя_і_тапалогія" style="font-size:114%;margin:0 5em"><a href="/wiki/%D0%93%D0%B5%D0%B0%D0%BC%D0%B5%D1%82%D1%80%D1%8B%D1%8F" title="Геаметрыя">Геаметрыя</a> і <a 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href="/wiki/%D0%94%D1%8B%D1%84%D0%B5%D1%80%D1%8D%D0%BD%D1%86%D1%8B%D1%8F%D0%BB%D1%8C%D0%BD%D0%B0%D1%8F_%D0%B3%D0%B5%D0%B0%D0%BC%D0%B5%D1%82%D1%80%D1%8B%D1%8F" title="Дыферэнцыяльная геаметрыя">Дыферэнцыяльная геаметрыя</a></li> <li><a href="/wiki/%D0%95%D1%9E%D0%BA%D0%BB%D1%96%D0%B4%D0%B0%D0%B2%D0%B0_%D0%B3%D0%B5%D0%B0%D0%BC%D0%B5%D1%82%D1%80%D1%8B%D1%8F" class="mw-redirect" title="Еўклідава геаметрыя">Еўклідава геаметрыя</a></li> <li><a href="/w/index.php?title=%D0%9D%D0%B5%D0%B5%D1%9E%D0%BA%D0%BB%D1%96%D0%B4%D0%B0%D0%B2%D0%B0_%D0%B3%D0%B5%D0%B0%D0%BC%D0%B5%D1%82%D1%80%D1%8B%D1%8F&action=edit&redlink=1" class="new" title="Нееўклідава геаметрыя (няма такой старонкі)">Нееўклідава геаметрыя</a></li> <li><a href="/wiki/%D0%9F%D0%BB%D0%B0%D0%BD%D1%96%D0%BC%D0%B5%D1%82%D1%80%D1%8B%D1%8F" title="Планіметрыя">Планіметрыя</a></li> <li><a href="/wiki/%D0%A1%D1%82%D1%8D%D1%80%D1%8D%D0%B0%D0%BC%D0%B5%D1%82%D1%80%D1%8B%D1%8F" title="Стэрэаметрыя">Стэрэаметрыя</a></li> <li><a href="/wiki/%D0%A2%D1%80%D1%8B%D0%B3%D0%B0%D0%BD%D0%B0%D0%BC%D0%B5%D1%82%D1%80%D1%8B%D1%8F" title="Трыганаметрыя">Трыганаметрыя</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1px"><a href="/wiki/%D0%A2%D0%B0%D0%BF%D0%B0%D0%BB%D0%BE%D0%B3%D1%96%D1%8F" title="Тапалогія">Тапалогія</a></th><td class="navbox-list navbox-even hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/w/index.php?title=%D0%90%D0%B3%D1%83%D0%BB%D1%8C%D0%BD%D0%B0%D1%8F_%D1%82%D0%B0%D0%BF%D0%B0%D0%BB%D0%BE%D0%B3%D1%96%D1%8F&action=edit&redlink=1" class="new" title="Агульная тапалогія (няма такой старонкі)">Агульная тапалогія</a></li> <li><a href="/w/index.php?title=%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0%D1%96%D1%87%D0%BD%D0%B0%D1%8F_%D1%82%D0%B0%D0%BF%D0%B0%D0%BB%D0%BE%D0%B3%D1%96%D1%8F&action=edit&redlink=1" class="new" title="Алгебраічная тапалогія (няма такой старонкі)">Алгебраічная тапалогія</a></li> <li><a href="/w/index.php?title=%D0%94%D1%8B%D1%84%D0%B5%D1%80%D1%8D%D0%BD%D1%86%D1%8B%D1%8F%D0%BB%D1%8C%D0%BD%D0%B0%D1%8F_%D1%82%D0%B0%D0%BF%D0%B0%D0%BB%D0%BE%D0%B3%D1%96%D1%8F&action=edit&redlink=1" class="new" title="Дыферэнцыяльная тапалогія (няма такой старонкі)">Дыферэнцыяльная тапалогія</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><td class="navbox-list navbox-odd" style="width:100%;padding:0px"><div style="padding:0em 0.25em"></div><table class="nowraplinks collapsible collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Дыскрэтная_матэматыка" style="font-size:114%;margin:0 5em"><a href="/wiki/%D0%94%D1%8B%D1%81%D0%BA%D1%80%D1%8D%D1%82%D0%BD%D0%B0%D1%8F_%D0%BC%D0%B0%D1%82%D1%8D%D0%BC%D0%B0%D1%82%D1%8B%D0%BA%D0%B0" title="Дыскрэтная матэматыка">Дыскрэтная матэматыка</a></div></th></tr><tr><td class="navbox-list navbox-odd hlist hlist-items-nowrap" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%D0%9A%D0%B0%D0%BC%D0%B1%D1%96%D0%BD%D0%B0%D1%82%D0%BE%D1%80%D1%8B%D0%BA%D0%B0" title="Камбінаторыка">Камбінаторыка</a></li> <li><a href="/wiki/%D0%A2%D1%8D%D0%BE%D1%80%D1%8B%D1%8F_%D0%B3%D1%80%D0%B0%D1%84%D0%B0%D1%9E" title="Тэорыя графаў">Тэорыя графаў</a></li> <li><a href="/w/index.php?title=%D0%91%D1%83%D0%BB%D0%B5%D0%B2%D0%B0_%D0%B0%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0&action=edit&redlink=1" class="new" title="Булева алгебра (няма такой старонкі)">Булева алгебра</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><td class="navbox-list navbox-odd" style="width:100%;padding:0px"><div style="padding:0em 0.25em"></div><table class="nowraplinks collapsible collapsed navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><div id="Прыкладная_матэматыка" style="font-size:114%;margin:0 5em"><a href="/wiki/%D0%9F%D1%80%D1%8B%D0%BA%D0%BB%D0%B0%D0%B4%D0%BD%D0%B0%D1%8F_%D0%BC%D0%B0%D1%82%D1%8D%D0%BC%D0%B0%D1%82%D1%8B%D0%BA%D0%B0" title="Прыкладная матэматыка">Прыкладная матэматыка</a></div></th></tr><tr><td class="navbox-list navbox-odd hlist hlist-items-nowrap" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%D0%9C%D0%B0%D1%82%D1%8D%D0%BC%D0%B0%D1%82%D1%8B%D1%87%D0%BD%D0%B0%D1%8F_%D1%84%D1%96%D0%B7%D1%96%D0%BA%D0%B0" title="Матэматычная фізіка">Матэматычная фізіка</a></li> <li><a href="/w/index.php?title=%D0%9C%D0%B0%D1%82%D1%8D%D0%BC%D0%B0%D1%82%D1%8B%D1%87%D0%BD%D0%B0%D1%8F_%D1%85%D1%96%D0%BC%D1%96%D1%8F&action=edit&redlink=1" class="new" title="Матэматычная хімія (няма такой старонкі)">Матэматычная хімія</a></li> <li><a href="/wiki/%D0%9C%D0%B0%D1%82%D1%8D%D0%BC%D0%B0%D1%82%D1%8B%D1%87%D0%BD%D0%B0%D1%8F_%D1%81%D1%82%D0%B0%D1%82%D1%8B%D1%81%D1%82%D1%8B%D0%BA%D0%B0" title="Матэматычная статыстыка">Матэматычная статыстыка</a></li> <li><a href="/w/index.php?title=%D0%9C%D0%B0%D1%82%D1%8D%D0%BC%D0%B0%D1%82%D1%8B%D1%87%D0%BD%D0%B0%D0%B5_%D0%BC%D0%B0%D0%B4%D1%8D%D0%BB%D1%8F%D0%B2%D0%B0%D0%BD%D0%BD%D0%B5&action=edit&redlink=1" class="new" title="Матэматычнае мадэляванне (няма такой старонкі)">Матэматычнае мадэляванне</a></li> <li><a href="/w/index.php?title=%D0%A2%D1%8D%D0%BE%D1%80%D1%8B%D1%8F_%D0%B0%D0%BB%D0%B3%D0%B0%D1%80%D1%8B%D1%82%D0%BC%D0%B0%D1%9E&action=edit&redlink=1" class="new" title="Тэорыя алгарытмаў (няма такой старонкі)">Тэорыя алгарытмаў</a></li> <li><a href="/wiki/%D0%9B%D1%96%D0%BA%D0%B0%D0%B2%D1%8B%D1%8F_%D0%BC%D0%B5%D1%82%D0%B0%D0%B4%D1%8B" title="Лікавыя метады">Лікавыя метады</a></li> <li><a href="/wiki/%D0%9C%D0%B0%D1%82%D1%8D%D0%BC%D0%B0%D1%82%D1%8B%D1%87%D0%BD%D0%B0%D1%8F_%D1%8D%D0%BA%D0%B0%D0%BD%D0%BE%D0%BC%D1%96%D0%BA%D0%B0" title="Матэматычная эканоміка">Матэматычная эканоміка</a>, <a href="/w/index.php?title=%D0%A4%D1%96%D0%BD%D0%B0%D0%BD%D1%81%D0%B0%D0%B2%D0%B0%D1%8F_%D0%BC%D0%B0%D1%82%D1%8D%D0%BC%D0%B0%D1%82%D1%8B%D0%BA%D0%B0&action=edit&redlink=1" class="new" title="Фінансавая матэматыка (няма такой старонкі)">Фінансавая матэматыка</a></li> <li><a href="/wiki/%D0%A2%D1%8D%D0%BE%D1%80%D1%8B%D1%8F_%D1%96%D0%BC%D0%B0%D0%B2%D0%B5%D1%80%D0%BD%D0%B0%D1%81%D1%86%D0%B5%D0%B9" title="Тэорыя імавернасцей">Тэорыя імавернасцей</a></li> <li><a href="/w/index.php?title=%D0%94%D0%B0%D1%81%D0%BB%D0%B5%D0%B4%D0%B0%D0%B2%D0%B0%D0%BD%D0%BD%D0%B5_%D0%B0%D0%BF%D0%B5%D1%80%D0%B0%D1%86%D1%8B%D0%B9&action=edit&redlink=1" class="new" title="Даследаванне аперацый (няма такой старонкі)">Даследаванне аперацый</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr></tbody></table><div></div></td></tr><tr><td colspan="2" class="navbox-list navbox-even" style="width:100%;padding:0px"><div style="padding:0em 0.25em"><span style="white-space: nowrap;"><a href="/wiki/%D0%9C%D0%B0%D1%82%D1%8D%D0%BC%D0%B0%D1%82%D1%8B%D1%87%D0%BD%D0%B0%D1%8F_%D0%BB%D0%BE%D0%B3%D1%96%D0%BA%D0%B0" title="Матэматычная логіка">Матэматычная логіка</a> (<a href="/w/index.php?title=%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0_%D0%BB%D0%BE%D0%B3%D1%96%D0%BA%D1%96&action=edit&redlink=1" class="new" title="Алгебра логікі (няма такой старонкі)">алгебра логікі</a>) <span style="font-weight:bold"> · </span></span> <span style="white-space: nowrap;"><a href="/wiki/%D0%A2%D1%8D%D0%BE%D1%80%D1%8B%D1%8F_%D0%BB%D1%96%D0%BA%D0%B0%D1%9E" title="Тэорыя лікаў">Тэорыя лікаў</a> (<span class="mw-valign-baseline" typeof="mw:File"><a href="/wiki/%D0%92%D1%96%D0%BA%D1%96%D0%BF%D0%B5%D0%B4%D1%8B%D1%8F:%D0%94%D0%BE%D0%B1%D1%80%D1%8B%D1%8F_%D0%B0%D1%80%D1%82%D1%8B%D0%BA%D1%83%D0%BB%D1%8B" title="Добры артыкул"><img alt="✰" src="//upload.wikimedia.org/wikipedia/commons/thumb/2/20/Blue_star_unboxed.svg/13px-Blue_star_unboxed.svg.png" decoding="async" width="13" height="13" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/20/Blue_star_unboxed.svg/20px-Blue_star_unboxed.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/20/Blue_star_unboxed.svg/26px-Blue_star_unboxed.svg.png 2x" data-file-width="13" data-file-height="13" /></a></span> <a href="/wiki/%D0%90%D1%80%D1%8B%D1%84%D0%BC%D0%B5%D1%82%D1%8B%D0%BA%D0%B0" title="Арыфметыка">арыфметыка</a>)</span></div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div><a href="/wiki/%D0%9F%D0%B0%D1%80%D1%82%D0%B0%D0%BB:%D0%9D%D0%B0%D0%B2%D1%83%D0%BA%D0%B0" title="Партал:Навука">Партал «Навука»</a> | <a href="/w/index.php?title=%D0%9F%D0%B0%D1%80%D1%82%D0%B0%D0%BB:%D0%9C%D0%B0%D1%82%D1%8D%D0%BC%D0%B0%D1%82%D1%8B%D0%BA%D0%B0&action=edit&redlink=1" class="new" title="Партал:Матэматыка (няма такой старонкі)">Партал «Матэматыка»</a> | <a href="/wiki/%D0%9A%D0%B0%D1%82%D1%8D%D0%B3%D0%BE%D1%80%D1%8B%D1%8F:%D0%9C%D0%B0%D1%82%D1%8D%D0%BC%D0%B0%D1%82%D1%8B%D0%BA%D0%B0" title="Катэгорыя:Матэматыка">Катэгорыя «Матэматыка»</a></div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r4785216"></div><div role="navigation" class="navbox" aria-label="Навігацыйны шаблон" data-name="External links" style="padding:3px"><table class="nowraplinks hlist toCollapsibleCount navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="row" class="navbox-group" style="width:1px"><div style="padding: 0px 18px 0px 0px; width: 100%;"><div style="float: left;"><span class="noprint plainlinks nowrap" style="font-size:85%;"><span typeof="mw:File"><a href="/wiki/%D0%A8%D0%B0%D0%B1%D0%BB%D0%BE%D0%BD:%D0%92%D0%BE%D0%BD%D0%BA%D0%B0%D0%B2%D1%8B%D1%8F_%D1%81%D0%BF%D0%B0%D1%81%D1%8B%D0%BB%D0%BA%D1%96" title="Прагляд гэтага шаблона"><img alt="⚙️" src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c9/Wikipedia_interwiki_section_gear_icon.svg/14px-Wikipedia_interwiki_section_gear_icon.svg.png" decoding="async" width="14" height="14" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c9/Wikipedia_interwiki_section_gear_icon.svg/21px-Wikipedia_interwiki_section_gear_icon.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c9/Wikipedia_interwiki_section_gear_icon.svg/28px-Wikipedia_interwiki_section_gear_icon.svg.png 2x" data-file-width="14" data-file-height="14" /></a></span> </span></div>  Слоўнікі і энцыклапедыі</div></th><td class="navbox-list navbox-odd" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"><a rel="nofollow" class="external text" href="http://www.enciclopedia.cat/enciclopedies/gran-enciclopedia-catalana/EC-GEC-0076669.xml">Вялікая каталанская</a> · <a rel="nofollow" class="external text" href="https://snl.no/algebra">Вялікая нарвежская</a> · <a rel="nofollow" class="external text" href="https://bigenc.ru/c/algebra-41fc2e">Вялікая расійская (навукова-адукацыйны партал)</a> · <a href="https://be.wikisource.org/wiki/ru:%D0%91%D0%A1%D0%AD1/%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0" class="extiw" title="s:ru:БСЭ1/Алгебра">Вялікая савецкая (1 выд.)</a> · <a href="https://be.wikisource.org/wiki/ru:%D0%AD%D0%A1%D0%91%D0%95/%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0" class="extiw" title="s:ru:ЭСБЕ/Алгебра">Бракгаўза і Эфрона</a> · <a rel="nofollow" class="external text" href="https://www.krugosvet.ru/enc/nauka_i_tehnika/matematika/ALGEBRA.html">Кругасвет</a> · <a rel="nofollow" class="external text" href="https://www.larousse.fr/encyclopedie/divers/algèbre/19868">Ларуса</a> · <a href="https://be.wikisource.org/wiki/ru:%D0%9C%D0%AD%D0%A1%D0%91%D0%95/%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0" class="extiw" title="s:ru:МЭСБЕ/Алгебра">Малы Бракгаўза і Эфрона</a> · <a 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