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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_vi.wikipedia.org&uselang=vi" class=""><span>Quyên góp</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=%C4%90%E1%BA%B7c_bi%E1%BB%87t:M%E1%BB%9F_t%C3%A0i_kho%E1%BA%A3n&returnto=%C4%90%E1%BA%A1i+s%E1%BB%91+ph%E1%BB%95+d%E1%BB%A5ng" title="Bạn được khuyến khích mở tài khoản và đăng nhập; tuy nhiên, không bắt buộc phải có tài khoản" class=""><span>Tạo tài khoản</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=%C4%90%E1%BA%B7c_bi%E1%BB%87t:%C4%90%C4%83ng_nh%E1%BA%ADp&returnto=%C4%90%E1%BA%A1i+s%E1%BB%91+ph%E1%BB%95+d%E1%BB%A5ng" title="Đăng nhập sẽ có lợi hơn, tuy nhiên không bắt 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[o]" accesskey="o" class=""><span>Đăng nhập</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="Thêm tùy chọn" > <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="Công cụ cá nhân" > <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">Công cụ cá nhân</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal user-links-collapsible-item" title="Bảng chọn thành viên" > <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_vi.wikipedia.org&uselang=vi"><span>Quyên góp</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=%C4%90%E1%BA%B7c_bi%E1%BB%87t:M%E1%BB%9F_t%C3%A0i_kho%E1%BA%A3n&returnto=%C4%90%E1%BA%A1i+s%E1%BB%91+ph%E1%BB%95+d%E1%BB%A5ng" title="Bạn được khuyến khích mở tài khoản và đăng nhập; tuy nhiên, không bắt buộc phải có tài khoản"><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>Tạo tài khoản</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=%C4%90%E1%BA%B7c_bi%E1%BB%87t:%C4%90%C4%83ng_nh%E1%BA%ADp&returnto=%C4%90%E1%BA%A1i+s%E1%BB%91+ph%E1%BB%95+d%E1%BB%A5ng" title="Đăng nhập sẽ có lợi hơn, tuy nhiên không bắt buộc. [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>Đăng nhập</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"> Trang dành cho người dùng chưa đăng nhập <a href="/wiki/Tr%E1%BB%A3_gi%C3%BAp:Gi%E1%BB%9Bi_thi%E1%BB%87u" aria-label="Tìm hiểu thêm về sửa đổi"><span>tìm hiểu thêm</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/%C4%90%E1%BA%B7c_bi%E1%BB%87t:%C4%90%C3%B3ng_g%C3%B3p_c%E1%BB%A7a_t%C3%B4i" title="Danh sách các sửa đổi được thực hiện qua địa chỉ IP này [y]" accesskey="y"><span>Đóng góp</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/%C4%90%E1%BA%B7c_bi%E1%BB%87t:Th%E1%BA%A3o_lu%E1%BA%ADn_t%C3%B4i" title="Thảo luận với địa chỉ IP này [n]" accesskey="n"><span>Thảo luận cho địa chỉ IP này</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="Trang Web"> <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="Nội dung" 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">Nội dung</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">chuyển sang thanh bên</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">ẩn</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">Đầu</div> </a> </li> <li id="toc-Khái_niệm_cơ_bản" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Khái_niệm_cơ_bản"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Khái niệm cơ bản</span> </div> </a> <button aria-controls="toc-Khái_niệm_cơ_bản-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>Hiện/ẩn mục Khái niệm cơ bản</span> </button> <ul id="toc-Khái_niệm_cơ_bản-sublist" class="vector-toc-list"> <li id="toc-Đại_số" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Đại_số"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Đại số</span> </div> </a> <ul id="toc-Đại_số-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Phép_toán" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Phép_toán"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2</span> <span>Phép toán</span> </div> </a> <ul id="toc-Phép_toán-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Kiểu_của_đại_số" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Kiểu_của_đại_số"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.3</span> <span>Kiểu của đại số</span> </div> </a> <ul id="toc-Kiểu_của_đại_số-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Đại_số_con" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Đại_số_con"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Đại số con</span> </div> </a> <ul id="toc-Đại_số_con-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Tích_trực_tiếp" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Tích_trực_tiếp"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Tích trực tiếp</span> </div> </a> <ul id="toc-Tích_trực_tiếp-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Đồng_cấu_đại_số" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Đồng_cấu_đại_số"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Đồng cấu đại số</span> </div> </a> <ul id="toc-Đồng_cấu_đại_số-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Đa_tạp_'"`UNIQ--postMath-00000012-QINU`"'-đại_số" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Đa_tạp_'"`UNIQ--postMath-00000012-QINU`"'-đại_số"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Đa tạp '"`UNIQ--postMath-00000012-QINU`"'-đại số</span> </div> </a> <ul id="toc-Đa_tạp_'"`UNIQ--postMath-00000012-QINU`"'-đại_số-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Đại_số_tự_do" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Đại_số_tự_do"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Đại số tự do</span> </div> </a> <ul id="toc-Đại_số_tự_do-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Xem_thêm" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Xem_thêm"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Xem thêm</span> </div> </a> <ul id="toc-Xem_thêm-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Tham_khảo" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Tham_khảo"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Tham khảo</span> </div> </a> <ul id="toc-Tham_khảo-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="Nội dung" 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="Đóng mở mục lục" > <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">Đóng mở mục lục</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">Đại số phổ dụng</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="Xem bài viết trong ngôn ngữ khác. Bài có sẵn trong 33 ngôn ngữ" > <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-33" 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">33 ngôn ngữ</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%AC%D8%A8%D8%B1_%D8%B4%D8%A7%D9%85%D9%84" title="جبر شامل – Tiếng Ả Rập" lang="ar" hreflang="ar" data-title="جبر شامل" data-language-autonym="العربية" data-language-local-name="Tiếng Ả Rập" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Aljabar_universal" title="Aljabar universal – Tiếng Indonesia" lang="id" hreflang="id" data-title="Aljabar universal" data-language-autonym="Bahasa Indonesia" data-language-local-name="Tiếng Indonesia" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Algebra_universal" title="Algebra universal – Tiếng Mã Lai" lang="ms" hreflang="ms" data-title="Algebra universal" data-language-autonym="Bahasa Melayu" data-language-local-name="Tiếng Mã Lai" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%A3%D0%BD%D0%B8%D0%B2%D0%B5%D1%80%D1%81%D0%B0%D0%BB%D0%BD%D0%B0_%D0%B0%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0" title="Универсална алгебра – Tiếng Bulgaria" lang="bg" hreflang="bg" data-title="Универсална алгебра" data-language-autonym="Български" data-language-local-name="Tiếng Bulgaria" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/%C3%80lgebra_universal" title="Àlgebra universal – Tiếng Catalan" lang="ca" hreflang="ca" data-title="Àlgebra universal" data-language-autonym="Català" data-language-local-name="Tiếng Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%A3%D0%BD%D0%B8%D0%B2%D0%B5%D1%80%D1%81%D0%B0%D0%BB%D0%BB%C4%83_%D0%B0%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0" title="Универсаллă алгебра – Tiếng Chuvash" lang="cv" hreflang="cv" data-title="Универсаллă алгебра" data-language-autonym="Чӑвашла" data-language-local-name="Tiếng Chuvash" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Univerz%C3%A1ln%C3%AD_algebra" title="Univerzální algebra – Tiếng Séc" lang="cs" hreflang="cs" data-title="Univerzální algebra" data-language-autonym="Čeština" data-language-local-name="Tiếng Séc" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Universelle_Algebra" title="Universelle Algebra – Tiếng Đức" lang="de" hreflang="de" data-title="Universelle Algebra" data-language-autonym="Deutsch" data-language-local-name="Tiếng Đức" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Universaalalgebra" title="Universaalalgebra – Tiếng Estonia" lang="et" hreflang="et" data-title="Universaalalgebra" data-language-autonym="Eesti" data-language-local-name="Tiếng Estonia" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Universal_algebra" title="Universal algebra – Tiếng Anh" lang="en" hreflang="en" data-title="Universal algebra" data-language-autonym="English" data-language-local-name="Tiếng Anh" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/%C3%81lgebra_universal" title="Álgebra universal – Tiếng Tây Ban Nha" lang="es" hreflang="es" data-title="Álgebra universal" data-language-autonym="Español" data-language-local-name="Tiếng Tây Ban Nha" class="interlanguage-link-target"><span>Español</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_%D8%AC%D9%87%D8%A7%D9%86%DB%8C" title="جبر جهانی – Tiếng Ba Tư" lang="fa" hreflang="fa" data-title="جبر جهانی" data-language-autonym="فارسی" data-language-local-name="Tiếng Ba Tư" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Alg%C3%A8bre_universelle" title="Algèbre universelle – Tiếng Pháp" lang="fr" hreflang="fr" data-title="Algèbre universelle" data-language-autonym="Français" data-language-local-name="Tiếng Pháp" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%B3%B4%ED%8E%B8%EB%8C%80%EC%88%98%ED%95%99" title="보편대수학 – Tiếng Hàn" lang="ko" hreflang="ko" data-title="보편대수학" data-language-autonym="한국어" data-language-local-name="Tiếng Hàn" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Algebra_universal" title="Algebra universal – Tiếng Khoa Học Quốc Tế" lang="ia" hreflang="ia" data-title="Algebra universal" data-language-autonym="Interlingua" data-language-local-name="Tiếng Khoa Học Quốc Tế" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Algebra_universale" title="Algebra universale – Tiếng Italy" lang="it" hreflang="it" data-title="Algebra universale" data-language-autonym="Italiano" data-language-local-name="Tiếng Italy" class="interlanguage-link-target"><span>Italiano</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_%D7%90%D7%95%D7%A0%D7%99%D7%91%D7%A8%D7%A1%D7%9C%D7%99%D7%AA" title="אלגברה אוניברסלית – Tiếng Do Thái" lang="he" hreflang="he" data-title="אלגברה אוניברסלית" data-language-autonym="עברית" data-language-local-name="Tiếng Do Thái" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%A3%E1%83%9C%E1%83%98%E1%83%95%E1%83%94%E1%83%A0%E1%83%A1%E1%83%90%E1%83%9A%E1%83%A3%E1%83%A0%E1%83%98_%E1%83%90%E1%83%9A%E1%83%92%E1%83%94%E1%83%91%E1%83%A0%E1%83%90" title="უნივერსალური ალგებრა – Tiếng Georgia" lang="ka" hreflang="ka" data-title="უნივერსალური ალგებრა" data-language-autonym="ქართული" data-language-local-name="Tiếng Georgia" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Alj%C3%A8b_iniv%C3%A8s%C3%A8l" title="Aljèb inivèsèl – Tiếng Haiti" lang="ht" hreflang="ht" data-title="Aljèb inivèsèl" data-language-autonym="Kreyòl ayisyen" data-language-local-name="Tiếng Haiti" class="interlanguage-link-target"><span>Kreyòl ayisyen</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Universele_algebra" title="Universele algebra – Tiếng Hà Lan" lang="nl" hreflang="nl" data-title="Universele algebra" data-language-autonym="Nederlands" data-language-local-name="Tiếng Hà Lan" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E6%99%AE%E9%81%8D%E4%BB%A3%E6%95%B0%E5%AD%A6" title="普遍代数学 – Tiếng Nhật" lang="ja" hreflang="ja" data-title="普遍代数学" data-language-autonym="日本語" data-language-local-name="Tiếng Nhật" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%D8%B9%D8%A7%D9%84%D9%85%DB%8C_%D8%A7%D9%84%D8%AC%D8%A8%D8%B1%D8%A7" title="عالمی الجبرا – Western Punjabi" lang="pnb" hreflang="pnb" data-title="عالمی 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-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Algebra_uniwersalna" title="Algebra uniwersalna – Tiếng Ba Lan" lang="pl" hreflang="pl" data-title="Algebra uniwersalna" data-language-autonym="Polski" data-language-local-name="Tiếng Ba Lan" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/%C3%81lgebra_universal" title="Álgebra universal – Tiếng Bồ Đào Nha" lang="pt" hreflang="pt" data-title="Álgebra universal" data-language-autonym="Português" data-language-local-name="Tiếng Bồ Đào Nha" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Algebr%C4%83_universal%C4%83" title="Algebră universală – Tiếng Romania" lang="ro" hreflang="ro" data-title="Algebră universală" data-language-autonym="Română" data-language-local-name="Tiếng Romania" 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%A3%D0%BD%D0%B8%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" title="Универсальная алгебра – Tiếng Nga" lang="ru" hreflang="ru" data-title="Универсальная алгебра" data-language-autonym="Русский" data-language-local-name="Tiếng Nga" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Universell_algebra" title="Universell algebra – Tiếng Thụy Điển" lang="sv" hreflang="sv" data-title="Universell algebra" data-language-autonym="Svenska" data-language-local-name="Tiếng Thụy Điển" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Evrensel_cebir" title="Evrensel cebir – Tiếng Thổ Nhĩ Kỳ" lang="tr" hreflang="tr" data-title="Evrensel cebir" data-language-autonym="Türkçe" data-language-local-name="Tiếng Thổ Nhĩ Kỳ" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A3%D0%BD%D1%96%D0%B2%D0%B5%D1%80%D1%81%D0%B0%D0%BB%D1%8C%D0%BD%D0%B0_%D0%B0%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0" title="Універсальна алгебра – Tiếng Ukraina" lang="uk" hreflang="uk" data-title="Універсальна алгебра" data-language-autonym="Українська" data-language-local-name="Tiếng Ukraina" 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%B9%D8%A7%D9%84%D9%85%DB%8C_%D8%A7%D9%84%D8%AC%D8%A8%D8%B1%D8%A7" title="عالمی الجبرا – Tiếng Urdu" lang="ur" hreflang="ur" data-title="عالمی الجبرا" data-language-autonym="اردو" data-language-local-name="Tiếng Urdu" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-war mw-list-item"><a href="https://war.wikipedia.org/wiki/Alhebra_unibersal" title="Alhebra unibersal – Tiếng Waray" lang="war" hreflang="war" data-title="Alhebra unibersal" data-language-autonym="Winaray" data-language-local-name="Tiếng Waray" class="interlanguage-link-target"><span>Winaray</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E6%B3%9B%E4%BB%A3%E6%95%B8" title="泛代數 – Tiếng Quảng Đông" lang="yue" hreflang="yue" data-title="泛代數" data-language-autonym="粵語" data-language-local-name="Tiếng Quảng Đông" class="interlanguage-link-target"><span>粵語</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E6%B3%9B%E4%BB%A3%E6%95%B0" title="泛代数 – Tiếng Trung" lang="zh" hreflang="zh" data-title="泛代数" data-language-autonym="中文" data-language-local-name="Tiếng Trung" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q1636734#sitelinks-wikipedia" title="Sửa liên kết giữa ngôn ngữ" class="wbc-editpage">Sửa liên kết</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Không gian tên"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/%C4%90%E1%BA%A1i_s%E1%BB%91_ph%E1%BB%95_d%E1%BB%A5ng" title="Xem bài viết [c]" accesskey="c"><span>Bài viết</span></a></li><li id="ca-talk" class="new vector-tab-noicon mw-list-item"><a href="/w/index.php?title=Th%E1%BA%A3o_lu%E1%BA%ADn:%C4%90%E1%BA%A1i_s%E1%BB%91_ph%E1%BB%95_d%E1%BB%A5ng&action=edit&redlink=1" rel="discussion" class="new" title="Thảo luận về trang này (trang không tồn tại) [t]" accesskey="t"><span>Thảo luận</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown emptyPortlet" > <input type="checkbox" id="vector-variants-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-variants-dropdown" class="vector-dropdown-checkbox " aria-label="Thay đổi biến thể ngôn ngữ" > <label id="vector-variants-dropdown-label" for="vector-variants-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">Tiếng Việt</span> </label> <div class="vector-dropdown-content"> <div id="p-variants" class="vector-menu mw-portlet mw-portlet-variants emptyPortlet" > 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<div id="vector-page-tools-unpinned-container" class="vector-unpinned-container"> <div id="vector-page-tools" class="vector-page-tools vector-pinnable-element"> <div class="vector-pinnable-header vector-page-tools-pinnable-header vector-pinnable-header-unpinned" data-feature-name="page-tools-pinned" data-pinnable-element-id="vector-page-tools" data-pinned-container-id="vector-page-tools-pinned-container" data-unpinned-container-id="vector-page-tools-unpinned-container" > <div class="vector-pinnable-header-label">Công cụ</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">chuyển sang thanh bên</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">ẩn</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="Thêm tùy chọn" > <div class="vector-menu-heading"> Tác vụ </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-more-view" class="selected vector-more-collapsible-item mw-list-item"><a href="/wiki/%C4%90%E1%BA%A1i_s%E1%BB%91_ph%E1%BB%95_d%E1%BB%A5ng"><span>Đọc</span></a></li><li id="ca-more-ve-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=%C4%90%E1%BA%A1i_s%E1%BB%91_ph%E1%BB%95_d%E1%BB%A5ng&veaction=edit" title="Sửa đổi trang này [v]" accesskey="v"><span>Sửa đổi</span></a></li><li id="ca-more-edit" class="collapsible vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=%C4%90%E1%BA%A1i_s%E1%BB%91_ph%E1%BB%95_d%E1%BB%A5ng&action=edit" title="Sửa đổi mã nguồn của trang này [e]" accesskey="e"><span>Sửa mã nguồn</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a 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href="/wiki/%C4%90%E1%BA%B7c_bi%E1%BB%87t:Trang_%C4%91%E1%BA%B7c_bi%E1%BB%87t" title="Một danh sách chứa tất cả trang đặc biệt [q]" accesskey="q"><span>Trang đặc biệt</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=%C4%90%E1%BA%A1i_s%E1%BB%91_ph%E1%BB%95_d%E1%BB%A5ng&oldid=63034772" title="Liên kết thường trực đến phiên bản này của trang"><span>Liên kết thường trực</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=%C4%90%E1%BA%A1i_s%E1%BB%91_ph%E1%BB%95_d%E1%BB%A5ng&action=info" title="Thêm chi tiết về trang này"><span>Thông tin trang</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=%C4%90%E1%BA%B7c_bi%E1%BB%87t:Tr%C3%ADch_d%E1%BA%ABn&page=%C4%90%E1%BA%A1i_s%E1%BB%91_ph%E1%BB%95_d%E1%BB%A5ng&id=63034772&wpFormIdentifier=titleform" title="Hướng dẫn cách trích dẫn trang này"><span>Trích dẫn trang này</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=%C4%90%E1%BA%B7c_bi%E1%BB%87t:UrlShortener&url=https%3A%2F%2Fvi.wikipedia.org%2Fwiki%2F%25C4%2590%25E1%25BA%25A1i_s%25E1%25BB%2591_ph%25E1%25BB%2595_d%25E1%25BB%25A5ng"><span>Lấy URL ngắn gọn</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=%C4%90%E1%BA%B7c_bi%E1%BB%87t:QrCode&url=https%3A%2F%2Fvi.wikipedia.org%2Fwiki%2F%25C4%2590%25E1%25BA%25A1i_s%25E1%25BB%2591_ph%25E1%25BB%2595_d%25E1%25BB%25A5ng"><span>Tải mã QR</span></a></li> </ul> </div> </div> <div id="p-coll-print_export" class="vector-menu mw-portlet mw-portlet-coll-print_export" > <div class="vector-menu-heading"> In và xuất </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="coll-create_a_book" class="mw-list-item"><a href="/w/index.php?title=%C4%90%E1%BA%B7c_bi%E1%BB%87t:S%C3%A1ch&bookcmd=book_creator&referer=%C4%90%E1%BA%A1i+s%E1%BB%91+ph%E1%BB%95+d%E1%BB%A5ng"><span>Tạo một quyển sách</span></a></li><li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=%C4%90%E1%BA%B7c_bi%E1%BB%87t:DownloadAsPdf&page=%C4%90%E1%BA%A1i_s%E1%BB%91_ph%E1%BB%95_d%E1%BB%A5ng&action=show-download-screen"><span>Tải dưới dạng PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=%C4%90%E1%BA%A1i_s%E1%BB%91_ph%E1%BB%95_d%E1%BB%A5ng&printable=yes" title="Bản để in ra của trang [p]" accesskey="p"><span>Bản để in ra</span></a></li> </ul> </div> </div> <div id="p-wikibase-otherprojects" class="vector-menu mw-portlet mw-portlet-wikibase-otherprojects" > <div class="vector-menu-heading"> Tại dự án khác </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q1636734" title="Liên kết đến khoản mục kết nối trong kho dữ liệu [g]" accesskey="g"><span>Khoản mục Wikidata</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> </div> </div> </div> <div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="Công cụ trang"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Giao diện"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Giao diện</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">chuyển sang thanh bên</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">ẩn</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">Bách khoa toàn thư mở Wikipedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="vi" dir="ltr"><p><b>Đại số phổ dụng</b> thường gọi tắt là <b>đại số</b> là một cấu trúc đại số tổng quát nhất. Khái niệm đại số phổ dụng bao gồm tất cả các cấu trúc đại số đã biết như <i>nhóm</i>, <i>nửa nhóm</i>, <i>vành</i>, <i>trường</i>,... </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Khái_niệm_cơ_bản"><span id="Kh.C3.A1i_ni.E1.BB.87m_c.C6.A1_b.E1.BA.A3n"></span>Khái niệm cơ bản</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%C4%90%E1%BA%A1i_s%E1%BB%91_ph%E1%BB%95_d%E1%BB%A5ng&veaction=edit&section=1" title="Sửa đổi phần “Khái niệm cơ bản”" class="mw-editsection-visualeditor"><span>sửa</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%C4%90%E1%BA%A1i_s%E1%BB%91_ph%E1%BB%95_d%E1%BB%A5ng&action=edit&section=1" title="Sửa mã nguồn tại đề mục: Khái niệm cơ bản"><span>sửa mã nguồn</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Đại_số"><span id=".C4.90.E1.BA.A1i_s.E1.BB.91"></span>Đại số</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%C4%90%E1%BA%A1i_s%E1%BB%91_ph%E1%BB%95_d%E1%BB%A5ng&veaction=edit&section=2" title="Sửa đổi phần “Đại số”" class="mw-editsection-visualeditor"><span>sửa</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%C4%90%E1%BA%A1i_s%E1%BB%91_ph%E1%BB%95_d%E1%BB%A5ng&action=edit&section=2" title="Sửa mã nguồn tại đề mục: Đại số"><span>sửa mã nguồn</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Một <b>đại số phổ dụng</b>, gọi tắt là đại số là một cặp <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,\Omega )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>A</mi> <mo>,</mo> <mi mathvariant="normal">Ω</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (A,\Omega )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/68e4066ec06b49f6f97d9644010299adf92a75c7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.264ex; height:2.843ex;" alt="{\displaystyle (A,\Omega )}"></span>, trong đó A là một tập hợp không rỗng, được gọi là tập nền và <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 \Omega }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Ω</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Omega }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/24b0d5ca6f381068d756f6337c08e0af9d1eeb6f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.678ex; height:2.176ex;" alt="{\displaystyle \Omega }"></span> là tập hợp (hữu hạn hoặc vô hạn) các phép toán trên <i>A</i>. </p> <div class="mw-heading mw-heading3"><h3 id="Phép_toán"><span id="Ph.C3.A9p_to.C3.A1n"></span>Phép toán</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%C4%90%E1%BA%A1i_s%E1%BB%91_ph%E1%BB%95_d%E1%BB%A5ng&veaction=edit&section=3" title="Sửa đổi phần “Phép toán”" class="mw-editsection-visualeditor"><span>sửa</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%C4%90%E1%BA%A1i_s%E1%BB%91_ph%E1%BB%95_d%E1%BB%A5ng&action=edit&section=3" title="Sửa mã nguồn tại đề mục: Phép toán"><span>sửa mã nguồn</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Phép toán <i>n</i> ngôi <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 \omega }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ω</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \omega }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/48eff443f9de7a985bb94ca3bde20813ea737be8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.446ex; height:1.676ex;" alt="{\displaystyle \omega }"></span> trên <i>A</i> với <i>n</i> <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 \geq }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>≥</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \geq }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bcef7c0e95bb77a35fd1a874ca91f425215f3c26" 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 \geq }"></span> 1, <i>n</i> <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 \in \mathbb {N} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∈</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">N</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \in \mathbb {N} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a0a1e18ae51b234b66b365374bd3c614ce9f9420" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.874ex; height:2.176ex;" alt="{\displaystyle \in \mathbb {N} }"></span> là ánh xạ: </p> <dl><dd><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 \omega :A^{n}\to A}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ω</mi> <mo>:</mo> <msup> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> <mo stretchy="false">→</mo> <mi>A</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \omega :A^{n}\to A}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d696884a09205334699d0db686742a43a8fec240" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:11.702ex; height:2.343ex;" alt="{\displaystyle \omega :A^{n}\to A}"></span> <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 (a_{1},a_{2},...,a_{n})\mapsto a_{1}a_{2}...a_{n}\omega }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mo stretchy="false">↦</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>.</mo> <mo>.</mo> <mo>.</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mi>ω</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (a_{1},a_{2},...,a_{n})\mapsto a_{1}a_{2}...a_{n}\omega }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cb16e7a3ee164dba45b25071221627d0d4f52ca8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:30.207ex; height:2.843ex;" alt="{\displaystyle (a_{1},a_{2},...,a_{n})\mapsto a_{1}a_{2}...a_{n}\omega }"></span></dd></dl></dd></dl></dd></dl> <p>Trong đó, ký hiệu <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_{1}a_{2}...a_{n}\omega }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>.</mo> <mo>.</mo> <mo>.</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mi>ω</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a_{1}a_{2}...a_{n}\omega }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/aabe3c29c679f139cd454fa760cfe955eb67a4cb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:11.564ex; height:2.009ex;" alt="{\displaystyle a_{1}a_{2}...a_{n}\omega }"></span> thay cho <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 \omega (a_{1}a_{2}...a_{n})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ω</mi> <mo stretchy="false">(</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>.</mo> <mo>.</mo> <mo>.</mo> <msub> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \omega (a_{1}a_{2}...a_{n})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/083998dfbbe9f426b438f4121b3bb263c946a1eb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.373ex; height:2.843ex;" alt="{\displaystyle \omega (a_{1}a_{2}...a_{n})}"></span> là viết theo ký pháp Ba Lan. Để ký hiệu <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 \omega }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ω</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \omega }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/48eff443f9de7a985bb94ca3bde20813ea737be8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.446ex; height:1.676ex;" alt="{\displaystyle \omega }"></span> là phép toán n-ngôi ta viết <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 \omega \in {\Omega }_{n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ω</mi> <mo>∈</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Ω</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \omega \in {\Omega }_{n}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9a708cdfdac8cbfcdaf518fa35f223fb06389cd7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.183ex; height:2.509ex;" alt="{\displaystyle \omega \in {\Omega }_{n}}"></span> Ta cũng gọi là phép toán không ngôi <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 \omega \in {\Omega }_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ω</mi> <mo>∈</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Ω</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \omega \in {\Omega }_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3a64bd5053eb8e92c7da7a495ecf25cb7a47ad51" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.019ex; height:2.509ex;" alt="{\displaystyle \omega \in {\Omega }_{0}}"></span> là phép chọn một phần tử cố định trong <i>A</i>, kết quả phép chọn <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 \omega }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ω</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \omega }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/48eff443f9de7a985bb94ca3bde20813ea737be8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.446ex; height:1.676ex;" alt="{\displaystyle \omega }"></span> được ký hiệu là 1<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 \omega }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ω</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \omega }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/48eff443f9de7a985bb94ca3bde20813ea737be8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.446ex; height:1.676ex;" alt="{\displaystyle \omega }"></span> </p> <div class="mw-heading mw-heading3"><h3 id="Kiểu_của_đại_số"><span id="Ki.E1.BB.83u_c.E1.BB.A7a_.C4.91.E1.BA.A1i_s.E1.BB.91"></span>Kiểu của đại số</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%C4%90%E1%BA%A1i_s%E1%BB%91_ph%E1%BB%95_d%E1%BB%A5ng&veaction=edit&section=4" title="Sửa đổi phần “Kiểu của đại số”" class="mw-editsection-visualeditor"><span>sửa</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%C4%90%E1%BA%A1i_s%E1%BB%91_ph%E1%BB%95_d%E1%BB%A5ng&action=edit&section=4" title="Sửa mã nguồn tại đề mục: Kiểu của đại số"><span>sửa mã nguồn</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Cho <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,{\Omega _{A}})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>A</mi> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="normal">Ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </msub> </mrow> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (A,{\Omega _{A}})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/673ecf3dec8cd8b57eaffef1b2f45ebff873912a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.729ex; height:2.843ex;" alt="{\displaystyle (A,{\Omega _{A}})}"></span> là đại số với hữu hạn <a href="/wiki/Ph%C3%A9p_to%C3%A1n" title="Phép toán">phép toán</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 {\omega }_{1},...,{\omega }_{n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi>ω</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi>ω</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\omega }_{1},...,{\omega }_{n}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a2b8a579ce6d8dde2f1fefceedc3a89981614607" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:10.334ex; height:2.009ex;" alt="{\displaystyle {\omega }_{1},...,{\omega }_{n}}"></span>. Dãy các ngôi của các phép toán đó <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 (n({\omega }_{1}),...,n({\omega }_{1}))}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>n</mi> <mo stretchy="false">(</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi>ω</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo stretchy="false">)</mo> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <mi>n</mi> <mo stretchy="false">(</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi>ω</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo stretchy="false">)</mo> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (n({\omega }_{1}),...,n({\omega }_{1}))}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/da3521eb3c31f4c948fbc09ce91019bfcbd7c7ea" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:18.387ex; height:2.843ex;" alt="{\displaystyle (n({\omega }_{1}),...,n({\omega }_{1}))}"></span> được gọi là <a href="/w/index.php?title=Ki%E1%BB%83u_c%E1%BB%A7a_%C4%91%E1%BA%A1i_s%E1%BB%91&action=edit&redlink=1" class="new" title="Kiểu của đại số (trang không tồn tại)">kiểu của đại số</a> <i>A</i>. </p> <div class="mw-heading mw-heading2"><h2 id="Đại_số_con"><span id=".C4.90.E1.BA.A1i_s.E1.BB.91_con"></span>Đại số con</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%C4%90%E1%BA%A1i_s%E1%BB%91_ph%E1%BB%95_d%E1%BB%A5ng&veaction=edit&section=5" title="Sửa đổi phần “Đại số con”" class="mw-editsection-visualeditor"><span>sửa</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%C4%90%E1%BA%A1i_s%E1%BB%91_ph%E1%BB%95_d%E1%BB%A5ng&action=edit&section=5" title="Sửa mã nguồn tại đề mục: Đại số con"><span>sửa mã nguồn</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading2"><h2 id="Tích_trực_tiếp"><span id="T.C3.ADch_tr.E1.BB.B1c_ti.E1.BA.BFp"></span>Tích trực tiếp</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%C4%90%E1%BA%A1i_s%E1%BB%91_ph%E1%BB%95_d%E1%BB%A5ng&veaction=edit&section=6" title="Sửa đổi phần “Tích trực tiếp”" class="mw-editsection-visualeditor"><span>sửa</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%C4%90%E1%BA%A1i_s%E1%BB%91_ph%E1%BB%95_d%E1%BB%A5ng&action=edit&section=6" title="Sửa mã nguồn tại đề mục: Tích trực tiếp"><span>sửa mã nguồn</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading2"><h2 id="Đồng_cấu_đại_số"><span id=".C4.90.E1.BB.93ng_c.E1.BA.A5u_.C4.91.E1.BA.A1i_s.E1.BB.91"></span>Đồng cấu đại số</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%C4%90%E1%BA%A1i_s%E1%BB%91_ph%E1%BB%95_d%E1%BB%A5ng&veaction=edit&section=7" title="Sửa đổi phần “Đồng cấu đại số”" class="mw-editsection-visualeditor"><span>sửa</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%C4%90%E1%BA%A1i_s%E1%BB%91_ph%E1%BB%95_d%E1%BB%A5ng&action=edit&section=7" title="Sửa mã nguồn tại đề mục: Đồng cấu đại số"><span>sửa mã nguồn</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading2"><h2 id="Đa_tạp_'"`UNIQ--postMath-00000012-QINU`"'-đại_số"><span id=".C4.90a_t.E1.BA.A1p_.7F.27.22.60UNIQ--postMath-00000012-QINU.60.22.27.7F-.C4.91.E1.BA.A1i_s.E1.BB.91"></span>Đa tạp <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 \omega }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ω</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \omega }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/48eff443f9de7a985bb94ca3bde20813ea737be8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.446ex; height:1.676ex;" alt="{\displaystyle \omega }"></span>-đại số</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%C4%90%E1%BA%A1i_s%E1%BB%91_ph%E1%BB%95_d%E1%BB%A5ng&veaction=edit&section=8" title="Sửa đổi phần “Đa tạp '"`UNIQ--postMath-00000012-QINU`"'-đại số”" class="mw-editsection-visualeditor"><span>sửa</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%C4%90%E1%BA%A1i_s%E1%BB%91_ph%E1%BB%95_d%E1%BB%A5ng&action=edit&section=8" title="Sửa mã nguồn tại đề mục: Đa tạp '"`UNIQ--postMath-00000012-QINU`"'-đại số"><span>sửa mã nguồn</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading2"><h2 id="Đại_số_tự_do"><span id=".C4.90.E1.BA.A1i_s.E1.BB.91_t.E1.BB.B1_do"></span>Đại số tự do</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%C4%90%E1%BA%A1i_s%E1%BB%91_ph%E1%BB%95_d%E1%BB%A5ng&veaction=edit&section=9" title="Sửa đổi phần “Đại số tự do”" class="mw-editsection-visualeditor"><span>sửa</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%C4%90%E1%BA%A1i_s%E1%BB%91_ph%E1%BB%95_d%E1%BB%A5ng&action=edit&section=9" title="Sửa mã nguồn tại đề mục: Đại số tự do"><span>sửa mã nguồn</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading2"><h2 id="Xem_thêm"><span id="Xem_th.C3.AAm"></span>Xem thêm</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%C4%90%E1%BA%A1i_s%E1%BB%91_ph%E1%BB%95_d%E1%BB%A5ng&veaction=edit&section=10" title="Sửa đổi phần “Xem thêm”" class="mw-editsection-visualeditor"><span>sửa</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%C4%90%E1%BA%A1i_s%E1%BB%91_ph%E1%BB%95_d%E1%BB%A5ng&action=edit&section=10" title="Sửa mã nguồn tại đề mục: Xem thêm"><span>sửa mã nguồn</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/To%C3%A1n_h%E1%BB%8Dc" title="Toán học">Toán học</a></li></ul> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r70958518">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul ol,.mw-parser-output .hlist ul ul{display:inline}.mw-parser-output .hlist .mw-empty-li{display:none}.mw-parser-output .hlist dt::after{content:": "}.mw-parser-output .hlist dd::after,.mw-parser-output .hlist li::after{content:" · ";font-weight:bold}.mw-parser-output .hlist dd:last-child::after,.mw-parser-output .hlist dt:last-child::after,.mw-parser-output .hlist li:last-child::after{content:none}.mw-parser-output .hlist dd dd:first-child::before,.mw-parser-output .hlist dd dt:first-child::before,.mw-parser-output .hlist dd li:first-child::before,.mw-parser-output .hlist dt dd:first-child::before,.mw-parser-output .hlist dt dt:first-child::before,.mw-parser-output .hlist dt li:first-child::before,.mw-parser-output .hlist li dd:first-child::before,.mw-parser-output .hlist li dt:first-child::before,.mw-parser-output .hlist li li:first-child::before{content:" (";font-weight:normal}.mw-parser-output .hlist dd dd:last-child::after,.mw-parser-output .hlist dd dt:last-child::after,.mw-parser-output .hlist dd li:last-child::after,.mw-parser-output .hlist dt dd:last-child::after,.mw-parser-output .hlist dt dt:last-child::after,.mw-parser-output .hlist dt li:last-child::after,.mw-parser-output .hlist li dd:last-child::after,.mw-parser-output .hlist li dt:last-child::after,.mw-parser-output .hlist li li:last-child::after{content:")";font-weight:normal}.mw-parser-output .hlist ol{counter-reset:listitem}.mw-parser-output .hlist ol>li{counter-increment:listitem}.mw-parser-output .hlist ol>li::before{content:" "counter(listitem)"\a0 "}.mw-parser-output .hlist dd ol>li:first-child::before,.mw-parser-output .hlist dt ol>li:first-child::before,.mw-parser-output .hlist li ol>li:first-child::before{content:" ("counter(listitem)"\a0 "}</style><style data-mw-deduplicate="TemplateStyles:r71573313">.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}@media print{body.ns-0 .mw-parser-output .navbox{display:none!important}}</style></div><div role="navigation" class="navbox" aria-labelledby="Các_chủ_đề_chính_trong_đại_số" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="3"><div class="plainlinks hlist navbar mini"><ul><li class="nv-xem"><a href="/wiki/B%E1%BA%A3n_m%E1%BA%ABu:%C4%90%E1%BA%A1i_s%E1%BB%91" title="Bản mẫu:Đại số"><abbr title="Xem bản mẫu này">x</abbr></a></li><li class="nv-thảo luận"><a href="/wiki/Th%E1%BA%A3o_lu%E1%BA%ADn_B%E1%BA%A3n_m%E1%BA%ABu:%C4%90%E1%BA%A1i_s%E1%BB%91" title="Thảo luận Bản mẫu:Đại số"><abbr title="Thảo luận bản mẫu này">t</abbr></a></li><li class="nv-sửa"><a class="external text" href="https://vi.wikipedia.org/w/index.php?title=B%E1%BA%A3n_m%E1%BA%ABu:%C4%90%E1%BA%A1i_s%E1%BB%91&action=edit"><abbr title="Sửa bản mẫu này">s</abbr></a></li></ul></div><div id="Các_chủ_đề_chính_trong_đại_số" style="font-size:114%;margin:0 4em">Các chủ đề chính trong <a href="/wiki/%C4%90%E1%BA%A1i_s%E1%BB%91" title="Đại số">đại số</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">Các lĩnh vực chính</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/%C4%90%E1%BA%A1i_s%E1%BB%91_tr%E1%BB%ABu_t%C6%B0%E1%BB%A3ng" title="Đại số trừu tượng">Đại số trừu tượng</a></li> <li><a href="/wiki/L%C3%BD_thuy%E1%BA%BFt_ph%E1%BA%A1m_tr%C3%B9" title="Lý thuyết phạm trù">Lý thuyết phạm trù</a></li> <li><a href="/wiki/%C4%90%E1%BA%A1i_s%E1%BB%91_s%C6%A1_c%E1%BA%A5p" title="Đại số sơ cấp">Đại số sơ cấp</a></li> <li><a href="/w/index.php?title=L%C3%BD_thuy%E1%BA%BFt_K&action=edit&redlink=1" class="new" title="Lý thuyết K (trang không tồn tại)">Lý thuyết K</a></li> <li><a href="/wiki/%C4%90%E1%BA%A1i_s%E1%BB%91_giao_ho%C3%A1n" title="Đại số giao hoán">Đại số giao hoán</a></li> <li><a href="/w/index.php?title=V%C3%B2ng_kh%C3%B4ng_giao_ho%C3%A1n&action=edit&redlink=1" class="new" title="Vòng không giao hoán (trang không tồn tại)">Không giao hoán</a></li> <li><a href="/wiki/L%C3%BD_thuy%E1%BA%BFt_th%E1%BB%A9_t%E1%BB%B1" title="Lý thuyết thứ tự">Lý thuyết thứ tự</a></li> <li><a class="mw-selflink selflink">Đại số phổ dụng</a></li></ul> </div></td><td class="noviewer navbox-image" rowspan="6" style="width:1px;padding:0 0 0 2px"><div><figure class="mw-halign-none" typeof="mw:File"><a href="/wiki/T%E1%BA%ADp_tin:Mpl_example_Mandelbrot_set.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/28/Mpl_example_Mandelbrot_set.svg/180px-Mpl_example_Mandelbrot_set.svg.png" decoding="async" width="180" height="174" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/28/Mpl_example_Mandelbrot_set.svg/270px-Mpl_example_Mandelbrot_set.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/28/Mpl_example_Mandelbrot_set.svg/360px-Mpl_example_Mandelbrot_set.svg.png 2x" data-file-width="900" data-file-height="868" /></a><figcaption></figcaption></figure></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Các <a href="/wiki/C%E1%BA%A5u_tr%C3%BAc_%C4%91%E1%BA%A1i_s%E1%BB%91" title="Cấu trúc đại số">cấu trúc đại số</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Nh%C3%B3m_(to%C3%A1n_h%E1%BB%8Dc)" title="Nhóm (toán học)">Nhóm</a> (<a href="/wiki/L%C3%BD_thuy%E1%BA%BFt_nh%C3%B3m" title="Lý thuyết nhóm">Lý thuyết</a>)</li> <li><a href="/wiki/V%C3%A0nh" title="Vành">Vành</a> (<a href="/wiki/L%C3%BD_thuy%E1%BA%BFt_v%C3%A0nh" title="Lý thuyết vành">Lý thuyết</a>)</li> <li><a href="/w/index.php?title=Module_(to%C3%A1n_h%E1%BB%8Dc)&action=edit&redlink=1" class="new" title="Module (toán học) (trang không tồn tại)">Module</a> (<a href="/wiki/%C4%90%E1%BA%A1i_s%E1%BB%91_giao_ho%C3%A1n" title="Đại số giao hoán">Lý thuyết</a>)</li> <li><a href="/wiki/Tr%C6%B0%E1%BB%9Dng_(%C4%91%E1%BA%A1i_s%E1%BB%91)" title="Trường (đại số)">Trường</a></li> <li><a href="/wiki/V%C3%A0nh_%C4%91a_th%E1%BB%A9c" title="Vành đa thức">Vành đa thức</a> (<a href="/wiki/%C4%90a_th%E1%BB%A9c" title="Đa thức">Đa thức</a>, <a href="/wiki/Ph%C6%B0%C6%A1ng_tr%C3%ACnh_%C4%91%E1%BA%A1i_s%E1%BB%91" title="Phương trình đại số">Phương trình</a>)</li> <li><a href="/wiki/L%C3%BD_thuy%E1%BA%BFt_s%E1%BB%91_%C4%91%E1%BA%A1i_s%E1%BB%91" title="Lý thuyết số đại số">Lý thuyết số đại số</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%C4%90%E1%BA%A1i_s%E1%BB%91_tuy%E1%BA%BFn_t%C3%ADnh" title="Đại số tuyến tính">Đại số tuyến tính</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/Ma_tr%E1%BA%ADn_(to%C3%A1n_h%E1%BB%8Dc)" title="Ma trận (toán học)">Ma trận (lý thuyết)</a></li> <li><a href="/wiki/Kh%C3%B4ng_gian_vect%C6%A1" title="Không gian vectơ">Không gian vectơ</a> (<a href="/w/index.php?title=Vect%C6%A1_t%E1%BB%8Da_%C4%91%E1%BB%99&action=edit&redlink=1" class="new" title="Vectơ tọa độ (trang không tồn tại)">Vector</a>)</li> <li><a href="/w/index.php?title=M%C3%B4-%C4%91un_(to%C3%A1n_h%E1%BB%8Dc)&action=edit&redlink=1" class="new" title="Mô-đun (toán học) (trang không tồn tại)">Mô-đun</a></li> <li><a href="/w/index.php?title=Inner_product_space&action=edit&redlink=1" class="new" title="Inner product space (trang không tồn tại)">Inner product space</a> (<a href="/wiki/T%C3%ADch_v%C3%B4_h%C6%B0%E1%BB%9Bng" title="Tích vô hướng">Tích vô hướng</a>)</li> <li><a href="/wiki/Kh%C3%B4ng_gian_Hilbert" title="Không gian Hilbert">Không gian Hilbert</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/w/index.php?title=%C4%90%E1%BA%A1i_s%E1%BB%91_%C4%91a_tuy%E1%BA%BFn&action=edit&redlink=1" class="new" title="Đại số đa tuyến (trang không tồn tại)">Đại số đa tuyến</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/w/index.php?title=%C4%90%E1%BA%A1i_s%E1%BB%91_Tensor_algebra&action=edit&redlink=1" class="new" title="Đại số Tensor algebra (trang không tồn tại)">Đại số Tensor algebra</a></li> <li><a href="/w/index.php?title=Exterior_algebra&action=edit&redlink=1" class="new" title="Exterior algebra (trang không tồn tại)">Exterior algebra</a></li> <li><a href="/w/index.php?title=%C4%90%E1%BA%A1i_s%E1%BB%91_%C4%91%E1%BB%91i_x%E1%BB%A9ng&action=edit&redlink=1" class="new" title="Đại số đối xứng (trang không tồn tại)">Đại số đối xứng</a></li> <li><a href="/wiki/H%C3%ACnh_h%E1%BB%8Dc_%C4%91%E1%BA%A1i_s%E1%BB%91" title="Hình học đại số">Hình học đại số</a> (<a href="/w/index.php?title=Vect%C6%A1_%C4%91a_chi%E1%BB%81u&action=edit&redlink=1" class="new" title="Vectơ đa chiều (trang không tồn tại)">Vectơ đa chiều</a>)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Danh sách chủ đề</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/w/index.php?title=Danh_s%C3%A1ch_c%C3%A1c_ch%E1%BB%A7_%C4%91%E1%BB%81_%C4%91%E1%BA%A1i_s%E1%BB%91_tr%E1%BB%ABu_t%C6%B0%E1%BB%A3ng&action=edit&redlink=1" class="new" title="Danh sách các chủ đề đại số trừu tượng (trang không tồn tại)">Đại số trừu tượng</a></li> <li><a href="/w/index.php?title=Ph%C3%A1c_th%E1%BA%A3o_c%C3%A1c_c%E1%BA%A5u_tr%C3%BAc_%C4%91%E1%BA%A1i_s%E1%BB%91&action=edit&redlink=1" class="new" title="Phác thảo các cấu trúc đại số (trang không tồn tại)">Cấu trúc đại số</a></li> <li><a href="/w/index.php?title=Danh_s%C3%A1ch_c%C3%A1c_ch%E1%BB%A7_%C4%91%E1%BB%81_l%C3%BD_thuy%E1%BA%BFt_nh%C3%B3m&action=edit&redlink=1" class="new" title="Danh sách các chủ đề lý thuyết nhóm (trang không tồn tại)">Lý thuyết nhóm</a></li> <li><a href="/w/index.php?title=Danh_s%C3%A1ch_c%C3%A1c_ch%E1%BB%A7_%C4%91%E1%BB%81_%C4%91%E1%BA%A1i_s%E1%BB%91_tuy%E1%BA%BFn_t%C3%ADnh&action=edit&redlink=1" class="new" title="Danh sách các chủ đề đại số tuyến tính (trang không tồn tại)">Đại số tuyến tính</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Thuật ngữ</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/w/index.php?title=Danh_s%C3%A1ch_c%C3%A1c_ch%E1%BB%A7_%C4%91%E1%BB%81_%C4%91%E1%BA%A1i_s%E1%BB%91_tuy%E1%BA%BFn_t%C3%ADnh&action=edit&redlink=1" class="new" title="Danh sách các chủ đề đại số tuyến tính (trang không tồn tại)">Đại số tuyến tính</a></li> <li><a href="/w/index.php?title=B%E1%BA%A3ng_ch%C3%BA_gi%E1%BA%A3i_thu%E1%BA%ADt_ng%E1%BB%AF_l%C3%BD_thuy%E1%BA%BFt_tr%C6%B0%E1%BB%9Dng&action=edit&redlink=1" class="new" title="Bảng chú giải thuật ngữ lý thuyết trường (trang không tồn tại)">Lý thuyết trường</a></li> <li><a href="/w/index.php?title=B%E1%BA%A3ng_ch%C3%BA_gi%E1%BA%A3i_thu%E1%BA%ADt_ng%E1%BB%AF_l%C3%BD_thuy%E1%BA%BFt_v%C3%A0nh&action=edit&redlink=1" class="new" title="Bảng chú giải thuật ngữ lý thuyết vành (trang không tồn tại)">Lý thuyết vành</a></li> <li><a href="/w/index.php?title=B%E1%BA%A3ng_ch%C3%BA_gi%E1%BA%A3i_thu%E1%BA%ADt_ng%E1%BB%AF_l%C3%BD_thuy%E1%BA%BFt_th%E1%BB%A9_t%E1%BB%B1&action=edit&redlink=1" class="new" title="Bảng chú giải thuật ngữ lý thuyết thứ tự (trang không tồn tại)">Lý thuyết thứ tự</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="3" style="font-weight:bold;"><div> <ul><li><span typeof="mw:File"><span title="Thể loại"><img alt="Thể loại" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/48/Folder_Hexagonal_Icon.svg/16px-Folder_Hexagonal_Icon.svg.png" decoding="async" width="16" height="14" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/48/Folder_Hexagonal_Icon.svg/24px-Folder_Hexagonal_Icon.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/48/Folder_Hexagonal_Icon.svg/32px-Folder_Hexagonal_Icon.svg.png 2x" data-file-width="36" data-file-height="31" /></span></span> <a href="/wiki/Th%E1%BB%83_lo%E1%BA%A1i:%C4%90%E1%BA%A1i_s%E1%BB%91" title="Thể loại:Đại số">Thể loại</a></li> <li><span typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e0/Symbol_question.svg/16px-Symbol_question.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e0/Symbol_question.svg/23px-Symbol_question.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e0/Symbol_question.svg/31px-Symbol_question.svg.png 2x" data-file-width="180" data-file-height="185" /></span></span> <a href="/wiki/C%E1%BB%95ng_th%C3%B4ng_tin:To%C3%A1n_h%E1%BB%8Dc" title="Cổng thông tin:Toán học">Chủ đề</a></li> <li><span typeof="mw:File"><span title="Trang Wikibooks"><img alt="Trang Wikibooks" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikibooks-logo.svg/16px-Wikibooks-logo.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikibooks-logo.svg/24px-Wikibooks-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikibooks-logo.svg/32px-Wikibooks-logo.svg.png 2x" data-file-width="300" data-file-height="300" /></span></span> Wikibooks <ul><li><a href="https://en.wikibooks.org/wiki/vi:%C4%90%E1%BA%A1i_s%E1%BB%91" class="extiw" title="wikibooks:vi:Đại số">Sơ cấp</a></li> <li><a href="https://en.wikibooks.org/wiki/vi:%C4%90%E1%BA%A1i_s%E1%BB%91_tuy%E1%BA%BFn_t%C3%ADnh" class="extiw" title="wikibooks:vi:Đại số tuyến tính">Tuyến tính</a></li> <li><a href="https://en.wikibooks.org/wiki/vi:%C4%90%E1%BA%A1i_s%E1%BB%91_tr%E1%BB%ABu_t%C6%B0%E1%BB%A3ng" class="extiw" title="wikibooks:vi:Đại số trừu tượng">Trừu tượng</a></li></ul></li> <li><span typeof="mw:File"><span title="Trang Wikiversity"><img alt="Trang Wikiversity" src="//upload.wikimedia.org/wikipedia/commons/thumb/9/91/Wikiversity-logo.svg/16px-Wikiversity-logo.svg.png" decoding="async" width="16" height="13" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/91/Wikiversity-logo.svg/24px-Wikiversity-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/91/Wikiversity-logo.svg/32px-Wikiversity-logo.svg.png 2x" data-file-width="1000" data-file-height="800" /></span></span> <a href="https://en.wikiversity.org/wiki/%C4%90%E1%BA%A1i_s%E1%BB%91_tuy%E1%BA%BFn_t%C3%ADnh" class="extiw" title="wikiversity:Đại số tuyến tính">Wikiversity</a> <ul><li><a href="https://en.wikiversity.org/wiki/%C4%90%E1%BA%A1i_s%E1%BB%91_tuy%E1%BA%BFn_t%C3%ADnh" class="extiw" title="wikiversity:Đại số tuyến tính">Tuyến tính</a></li> <li><a href="https://en.wikiversity.org/wiki/C%E1%BA%A5u_tr%C3%BAc_%C4%91%E1%BA%A1i_s%E1%BB%91" class="extiw" title="wikiversity:Cấu trúc đại số">Trừu tượng</a></li></ul></li></ul> </div></td></tr></tbody></table></div> <div class="boilerplate metadata plainlinks" id="stub"><table class="metadata plainlinks stub" style="background: transparent;" role="presentation"><tbody><tr> <td><span typeof="mw:File"><a href="/wiki/Th%E1%BB%83_lo%E1%BA%A1i:S%C6%A1_khai_to%C3%A1n_h%E1%BB%8Dc" title="Thể loại:Sơ khai toán học"><img alt="Hình tượng sơ khai" src="//upload.wikimedia.org/wikipedia/commons/thumb/3/35/E-to-the-i-pi.svg/45px-E-to-the-i-pi.svg.png" decoding="async" width="45" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/35/E-to-the-i-pi.svg/68px-E-to-the-i-pi.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/35/E-to-the-i-pi.svg/90px-E-to-the-i-pi.svg.png 2x" data-file-width="512" data-file-height="453" /></a></span></td> <td><i>Bài viết liên quan đến <a href="/wiki/To%C3%A1n_h%E1%BB%8Dc" title="Toán học">toán học</a> này vẫn còn <a href="/wiki/Wikipedia:B%C3%A0i_s%C6%A1_khai" title="Wikipedia:Bài sơ khai">sơ khai</a>. Bạn có thể giúp Wikipedia <a class="external text" href="https://vi.wikipedia.org/w/index.php?title=%C4%90%E1%BA%A1i_s%E1%BB%91_ph%E1%BB%95_d%E1%BB%A5ng&veaction=edit">mở rộng nội dung</a> để bài được hoàn chỉnh hơn.</i><div class="plainlinks hlist navbar mini" style="position: absolute; right: 15px; display: none;"><ul><li class="nv-xem"><a href="/wiki/B%E1%BA%A3n_m%E1%BA%ABu:S%C6%A1_khai_to%C3%A1n_h%E1%BB%8Dc" title="Bản mẫu:Sơ khai toán học"><abbr title="Xem bản mẫu này">x</abbr></a></li><li class="nv-thảo luận"><a href="/w/index.php?title=Th%E1%BA%A3o_lu%E1%BA%ADn_B%E1%BA%A3n_m%E1%BA%ABu:S%C6%A1_khai_to%C3%A1n_h%E1%BB%8Dc&action=edit&redlink=1" class="new" title="Thảo luận Bản mẫu:Sơ khai toán học (trang không tồn tại)"><abbr title="Thảo luận bản mẫu này">t</abbr></a></li><li class="nv-sửa"><a class="external text" href="https://vi.wikipedia.org/w/index.php?title=B%E1%BA%A3n_m%E1%BA%ABu:S%C6%A1_khai_to%C3%A1n_h%E1%BB%8Dc&action=edit"><abbr title="Sửa bản mẫu này">s</abbr></a></li></ul></div></td> </tr></tbody></table></div> <p><br /> </p> <div class="mw-heading mw-heading2"><h2 id="Tham_khảo"><span id="Tham_kh.E1.BA.A3o"></span>Tham khảo</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%C4%90%E1%BA%A1i_s%E1%BB%91_ph%E1%BB%95_d%E1%BB%A5ng&veaction=edit&section=11" title="Sửa đổi phần “Tham khảo”" class="mw-editsection-visualeditor"><span>sửa</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%C4%90%E1%BA%A1i_s%E1%BB%91_ph%E1%BB%95_d%E1%BB%A5ng&action=edit&section=11" title="Sửa mã nguồn tại đề mục: Tham khảo"><span>sửa mã nguồn</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r71728118">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist" style="list-style-type: decimal;"> </div> <div class="boilerplate metadata plainlinks" id="stub"><table class="metadata plainlinks stub" style="background: transparent;" role="presentation"><tbody><tr> <td><i>Bài viết này vẫn còn <a href="/wiki/Wikipedia:B%C3%A0i_s%C6%A1_khai" title="Wikipedia:Bài sơ khai">sơ khai</a>. Bạn có thể giúp Wikipedia <a class="external text" href="https://vi.wikipedia.org/w/index.php?title=%C4%90%E1%BA%A1i_s%E1%BB%91_ph%E1%BB%95_d%E1%BB%A5ng&veaction=edit">mở rộng nội dung</a> để bài được hoàn chỉnh hơn.</i><div class="plainlinks hlist navbar mini" style="position: absolute; right: 15px; display: none;"><ul><li class="nv-xem"><a href="/wiki/B%E1%BA%A3n_m%E1%BA%ABu:S%C6%A1_khai" title="Bản mẫu:Sơ khai"><abbr title="Xem bản mẫu này">x</abbr></a></li><li class="nv-thảo luận"><a href="/wiki/Th%E1%BA%A3o_lu%E1%BA%ADn_B%E1%BA%A3n_m%E1%BA%ABu:S%C6%A1_khai" title="Thảo luận Bản mẫu:Sơ khai"><abbr title="Thảo luận bản mẫu này">t</abbr></a></li><li class="nv-sửa"><a class="external text" href="https://vi.wikipedia.org/w/index.php?title=B%E1%BA%A3n_m%E1%BA%ABu:S%C6%A1_khai&action=edit"><abbr title="Sửa bản mẫu này">s</abbr></a></li></ul></div></td> </tr></tbody></table></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Lấy từ “<a dir="ltr" href="https://vi.wikipedia.org/w/index.php?title=Đại_số_phổ_dụng&oldid=63034772">https://vi.wikipedia.org/w/index.php?title=Đại_số_phổ_dụng&oldid=63034772</a>”</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/%C4%90%E1%BA%B7c_bi%E1%BB%87t:Th%E1%BB%83_lo%E1%BA%A1i" title="Đặc biệt:Thể loại">Thể loại</a>: <ul><li><a href="/wiki/Th%E1%BB%83_lo%E1%BA%A1i:S%C6%A1_khai_to%C3%A1n_h%E1%BB%8Dc" title="Thể loại:Sơ khai toán học">Sơ khai toán học</a></li><li><a href="/wiki/Th%E1%BB%83_lo%E1%BA%A1i:C%E1%BA%A5u_tr%C3%BAc_%C4%91%E1%BA%A1i_s%E1%BB%91" title="Thể loại:Cấu trúc đại số">Cấu trúc đại số</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Thể loại ẩn: <ul><li><a href="/wiki/Th%E1%BB%83_lo%E1%BA%A1i:T%E1%BA%A5t_c%E1%BA%A3_b%C3%A0i_vi%E1%BA%BFt_s%C6%A1_khai" title="Thể loại:Tất cả bài viết sơ khai">Tất cả bài viết sơ khai</a></li><li><a href="/wiki/Th%E1%BB%83_lo%E1%BA%A1i:S%C6%A1_khai" title="Thể loại:Sơ khai">Sơ khai</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> Trang này được sửa đổi lần cuối vào ngày 13 tháng 7 năm 2020, 13:29.</li> <li id="footer-info-copyright">Văn bản được phát hành theo <a href="/wiki/Wikipedia:Nguy%C3%AAn_v%C4%83n_Gi%E1%BA%A5y_ph%C3%A9p_Creative_Commons_Ghi_c%C3%B4ng%E2%80%93Chia_s%E1%BA%BB_t%C6%B0%C6%A1ng_t%E1%BB%B1_phi%C3%AAn_b%E1%BA%A3n_4.0_Qu%E1%BB%91c_t%E1%BA%BF" title="Wikipedia:Nguyên văn Giấy phép Creative Commons Ghi công–Chia sẻ tương tự phiên bản 4.0 Quốc tế">Giấy phép Creative Commons Ghi công–Chia sẻ tương tự</a>; có thể áp dụng điều khoản bổ sung. 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