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<span class="vector-toc-numb">1</span> <span>Etymologie</span> </div> </a> <ul id="toc-Etymologie-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Afbakening" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Afbakening"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Afbakening</span> </div> </a> <ul id="toc-Afbakening-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Deelgebieden" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Deelgebieden"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Deelgebieden</span> </div> </a> <button aria-controls="toc-Deelgebieden-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>Deelgebieden-subkopje inklappen</span> </button> <ul id="toc-Deelgebieden-sublist" class="vector-toc-list"> <li id="toc-Elementaire_algebra" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Elementaire_algebra"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Elementaire algebra</span> </div> </a> <ul id="toc-Elementaire_algebra-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Abstracte_algebra" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Abstracte_algebra"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Abstracte algebra</span> </div> </a> <ul id="toc-Abstracte_algebra-sublist" class="vector-toc-list"> </ul> </li> </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="Inhoud" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown 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Beschikbaar in 169 talen" > <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-169" 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">169 talen</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 – Afrikaans" lang="af" hreflang="af" data-title="Algebra" data-language-autonym="Afrikaans" data-language-local-name="Afrikaans" 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 – Zwitserduits" lang="gsw" hreflang="gsw" data-title="Algebra" data-language-autonym="Alemannisch" data-language-local-name="Zwitserduits" 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 – Amhaars" lang="am" hreflang="am" data-title="አልጀብራ" data-language-autonym="አማርኛ" data-language-local-name="Amhaars" 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 – Aragonees" lang="an" hreflang="an" data-title="Alchebra" data-language-autonym="Aragonés" data-language-local-name="Aragonees" 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 – Oudengels" lang="ang" hreflang="ang" data-title="Rīmagiefung" data-language-autonym="Ænglisc" data-language-local-name="Oudengels" 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 – Angika" lang="anp" hreflang="anp" data-title="बीजगणित" data-language-autonym="अंगिका" data-language-local-name="Angika" 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 – Arabisch" lang="ar" hreflang="ar" data-title="الجبر" data-language-autonym="العربية" data-language-local-name="Arabisch" 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 – Egyptisch Arabisch" lang="arz" hreflang="arz" data-title="جبر" data-language-autonym="مصرى" data-language-local-name="Egyptisch Arabisch" 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 – Assamees" lang="as" hreflang="as" data-title="বীজগণিত" data-language-autonym="অসমীয়া" data-language-local-name="Assamees" 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 – Asturisch" lang="ast" hreflang="ast" data-title="Álxebra" data-language-autonym="Asturianu" data-language-local-name="Asturisch" 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 – Azerbeidzjaans" lang="az" hreflang="az" data-title="Cəbr" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbeidzjaans" 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 – Basjkiers" lang="ba" hreflang="ba" data-title="Алгебра" data-language-autonym="Башҡортса" data-language-local-name="Basjkiers" 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 – Samogitisch" lang="sgs" hreflang="sgs" data-title="Algebra" data-language-autonym="Žemaitėška" data-language-local-name="Samogitisch" 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 mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0" title="Алгебра – Belarussisch" lang="be" hreflang="be" data-title="Алгебра" data-language-autonym="Беларуская" data-language-local-name="Belarussisch" class="interlanguage-link-target"><span>Беларуская</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 – Bulgaars" lang="bg" hreflang="bg" data-title="Алгебра" data-language-autonym="Български" data-language-local-name="Bulgaars" 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 – Bengaals" lang="bn" hreflang="bn" data-title="বীজগণিত" data-language-autonym="বাংলা" data-language-local-name="Bengaals" 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། – Tibetaans" lang="bo" hreflang="bo" data-title="ཚབ་རྩིས།" data-language-autonym="བོད་ཡིག" data-language-local-name="Tibetaans" 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 – Bretons" lang="br" hreflang="br" data-title="Aljebr" data-language-autonym="Brezhoneg" data-language-local-name="Bretons" 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 – Bosnisch" lang="bs" hreflang="bs" data-title="Algebra" data-language-autonym="Bosanski" data-language-local-name="Bosnisch" 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 – Catalaans" lang="ca" hreflang="ca" data-title="Àlgebra" data-language-autonym="Català" data-language-local-name="Catalaans" 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 – Tsjetsjeens" lang="ce" hreflang="ce" data-title="Алгебра" data-language-autonym="Нохчийн" data-language-local-name="Tsjetsjeens" 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 – Soranî" lang="ckb" hreflang="ckb" data-title="جەبر" data-language-autonym="کوردی" data-language-local-name="Soranî" 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 – Corsicaans" lang="co" hreflang="co" data-title="Algebra" data-language-autonym="Corsu" data-language-local-name="Corsicaans" 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 – Tsjechisch" lang="cs" hreflang="cs" data-title="Algebra" data-language-autonym="Čeština" data-language-local-name="Tsjechisch" 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 – Tsjoevasjisch" lang="cv" hreflang="cv" data-title="Алгебра" data-language-autonym="Чӑвашла" data-language-local-name="Tsjoevasjisch" 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 – Welsh" lang="cy" hreflang="cy" data-title="Algebra" data-language-autonym="Cymraeg" data-language-local-name="Welsh" 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 – Deens" lang="da" hreflang="da" data-title="Algebra" data-language-autonym="Dansk" data-language-local-name="Deens" 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 – Duits" lang="de" hreflang="de" data-title="Algebra" data-language-autonym="Deutsch" data-language-local-name="Duits" 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 – Dimli" lang="diq" hreflang="diq" data-title="Cebir" data-language-autonym="Zazaki" data-language-local-name="Dimli" 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 – Grieks" lang="el" hreflang="el" data-title="Άλγεβρα" data-language-autonym="Ελληνικά" data-language-local-name="Grieks" 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="uitgelicht artikel"><a href="https://en.wikipedia.org/wiki/Algebra" title="Algebra – Engels" lang="en" hreflang="en" data-title="Algebra" data-language-autonym="English" data-language-local-name="Engels" 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 – Esperanto" lang="eo" hreflang="eo" data-title="Algebro" data-language-autonym="Esperanto" data-language-local-name="Esperanto" 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 – Spaans" lang="es" hreflang="es" data-title="Álgebra" data-language-autonym="Español" data-language-local-name="Spaans" 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 – Estisch" lang="et" hreflang="et" data-title="Algebra" data-language-autonym="Eesti" data-language-local-name="Estisch" 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 – Baskisch" lang="eu" hreflang="eu" data-title="Aljebra" data-language-autonym="Euskara" data-language-local-name="Baskisch" 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 – Perzisch" lang="fa" hreflang="fa" data-title="جبر" data-language-autonym="فارسی" data-language-local-name="Perzisch" 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 – Fins" lang="fi" hreflang="fi" data-title="Algebra" data-language-autonym="Suomi" data-language-local-name="Fins" 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 – Fijisch" lang="fj" hreflang="fj" data-title="Ivakavakadina" data-language-autonym="Na Vosa Vakaviti" data-language-local-name="Fijisch" 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 – Faeröers" lang="fo" hreflang="fo" data-title="Algebra" data-language-autonym="Føroyskt" data-language-local-name="Faeröers" 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 – Frans" lang="fr" hreflang="fr" data-title="Algèbre" data-language-autonym="Français" data-language-local-name="Frans" 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 – Noord-Fries" lang="frr" hreflang="frr" data-title="Algebra" data-language-autonym="Nordfriisk" data-language-local-name="Noord-Fries" 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 – Fries" lang="fy" hreflang="fy" data-title="Algebra" data-language-autonym="Frysk" data-language-local-name="Fries" 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 – Iers" lang="ga" hreflang="ga" data-title="Ailgéabar" data-language-autonym="Gaeilge" data-language-local-name="Iers" 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 – Ganyu" lang="gan" hreflang="gan" data-title="代數" data-language-autonym="贛語" data-language-local-name="Ganyu" 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 – Schots-Gaelisch" lang="gd" hreflang="gd" data-title="Ailseabra" data-language-autonym="Gàidhlig" data-language-local-name="Schots-Gaelisch" 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 – Galicisch" lang="gl" hreflang="gl" data-title="Álxebra" data-language-autonym="Galego" data-language-local-name="Galicisch" 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 – Guaraní" lang="gn" hreflang="gn" data-title="Álgebra" data-language-autonym="Avañe'ẽ" data-language-local-name="Guaraní" 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 – Gujarati" lang="gu" hreflang="gu" data-title="બીજગણિત" data-language-autonym="ગુજરાતી" data-language-local-name="Gujarati" 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 – Manx" lang="gv" hreflang="gv" data-title="Algeerey" data-language-autonym="Gaelg" data-language-local-name="Manx" 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 – Hausa" lang="ha" hreflang="ha" data-title="Algebra" data-language-autonym="Hausa" data-language-local-name="Hausa" 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 – Hebreeuws" lang="he" hreflang="he" data-title="אלגברה" data-language-autonym="עברית" data-language-local-name="Hebreeuws" 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 – Hindi" lang="hi" hreflang="hi" data-title="बीजगणित" data-language-autonym="हिन्दी" data-language-local-name="Hindi" 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 – Fijisch Hindi" lang="hif" hreflang="hif" data-title="Algebra" data-language-autonym="Fiji Hindi" data-language-local-name="Fijisch 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 – Kroatisch" lang="hr" hreflang="hr" data-title="Algebra" data-language-autonym="Hrvatski" data-language-local-name="Kroatisch" 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 – Haïtiaans Creools" lang="ht" hreflang="ht" data-title="Aljèb" data-language-autonym="Kreyòl ayisyen" data-language-local-name="Haïtiaans Creools" 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 – Hongaars" lang="hu" hreflang="hu" data-title="Algebra" data-language-autonym="Magyar" data-language-local-name="Hongaars" 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 – Armeens" lang="hy" hreflang="hy" data-title="Հանրահաշիվ" data-language-autonym="Հայերեն" data-language-local-name="Armeens" 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 – Interlingua" lang="ia" hreflang="ia" data-title="Algebra" data-language-autonym="Interlingua" data-language-local-name="Interlingua" 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 – Iban" lang="iba" hreflang="iba" data-title="Algebra" data-language-autonym="Jaku Iban" data-language-local-name="Iban" 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 – Indonesisch" lang="id" hreflang="id" data-title="Aljabar" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesisch" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-ie mw-list-item"><a href="https://ie.wikipedia.org/wiki/Algebra" title="Algebra – Interlingue" lang="ie" hreflang="ie" data-title="Algebra" data-language-autonym="Interlingue" data-language-local-name="Interlingue" class="interlanguage-link-target"><span>Interlingue</span></a></li><li class="interlanguage-link interwiki-ilo mw-list-item"><a href="https://ilo.wikipedia.org/wiki/Alhebra" title="Alhebra – Iloko" lang="ilo" hreflang="ilo" data-title="Alhebra" data-language-autonym="Ilokano" data-language-local-name="Iloko" 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 – Ingoesjetisch" lang="inh" hreflang="inh" data-title="Алгебра" data-language-autonym="ГӀалгӀай" data-language-local-name="Ingoesjetisch" 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 – Ido" lang="io" hreflang="io" data-title="Algebro" data-language-autonym="Ido" data-language-local-name="Ido" 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 – IJslands" lang="is" hreflang="is" data-title="Algebra" data-language-autonym="Íslenska" data-language-local-name="IJslands" 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 – Italiaans" lang="it" hreflang="it" data-title="Algebra" data-language-autonym="Italiano" data-language-local-name="Italiaans" 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 – Japans" lang="ja" hreflang="ja" data-title="代数学" data-language-autonym="日本語" data-language-local-name="Japans" 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 – Jamaicaans Creools" lang="jam" hreflang="jam" data-title="Aljibra" data-language-autonym="Patois" data-language-local-name="Jamaicaans Creools" 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 – Lojban" lang="jbo" hreflang="jbo" data-title="alxebra" data-language-autonym="La .lojban." data-language-local-name="Lojban" 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 – Javaans" lang="jv" hreflang="jv" data-title="Aljabar" data-language-autonym="Jawa" data-language-local-name="Javaans" 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 – Georgisch" lang="ka" hreflang="ka" data-title="ალგებრა" data-language-autonym="ქართული" data-language-local-name="Georgisch" 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 – Karakalpaks" lang="kaa" hreflang="kaa" data-title="Algebra" data-language-autonym="Qaraqalpaqsha" data-language-local-name="Karakalpaks" 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 – Kabylisch" lang="kab" hreflang="kab" data-title="Aljiber" data-language-autonym="Taqbaylit" data-language-local-name="Kabylisch" 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 – Kabardisch" lang="kbd" hreflang="kbd" data-title="Алгебрэ" data-language-autonym="Адыгэбзэ" data-language-local-name="Kabardisch" 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 – Kazachs" lang="kk" hreflang="kk" data-title="Алгебра" data-language-autonym="Қазақша" data-language-local-name="Kazachs" 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 – Kannada" lang="kn" hreflang="kn" data-title="ಬೀಜಗಣಿತ" data-language-autonym="ಕನ್ನಡ" data-language-local-name="Kannada" class="interlanguage-link-target"><span>ಕನ್ನಡ</span></a></li><li class="interlanguage-link interwiki-knc mw-list-item"><a href="https://knc.wikipedia.org/wiki/Algebra" title="Algebra – Central Kanuri" lang="knc" hreflang="knc" data-title="Algebra" data-language-autonym="Yerwa Kanuri" data-language-local-name="Central Kanuri" class="interlanguage-link-target"><span>Yerwa Kanuri</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 – Koreaans" lang="ko" hreflang="ko" data-title="대수학" data-language-autonym="한국어" data-language-local-name="Koreaans" 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 – Cornish" lang="kw" hreflang="kw" data-title="Aljebra" data-language-autonym="Kernowek" data-language-local-name="Cornish" 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 – Kirgizisch" lang="ky" hreflang="ky" data-title="Алгебра" data-language-autonym="Кыргызча" data-language-local-name="Kirgizisch" 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 – Latijn" lang="la" hreflang="la" data-title="Algebra" data-language-autonym="Latina" data-language-local-name="Latijn" 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 – Luganda" lang="lg" hreflang="lg" data-title="Aligebbula" data-language-autonym="Luganda" data-language-local-name="Luganda" 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 – Limburgs" lang="li" hreflang="li" data-title="Algebra" data-language-autonym="Limburgs" data-language-local-name="Limburgs" 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 – Ligurisch" lang="lij" hreflang="lij" data-title="Algebra" data-language-autonym="Ligure" data-language-local-name="Ligurisch" 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 – Lombardisch" lang="lmo" hreflang="lmo" data-title="Algebra" data-language-autonym="Lombard" data-language-local-name="Lombardisch" 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 – Laotiaans" lang="lo" hreflang="lo" data-title="ພຶດຊະຄະນິດ" data-language-autonym="ລາວ" data-language-local-name="Laotiaans" 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 – Litouws" lang="lt" hreflang="lt" data-title="Algebra" data-language-autonym="Lietuvių" data-language-local-name="Litouws" 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 – Lets" lang="lv" hreflang="lv" data-title="Algebra" data-language-autonym="Latviešu" data-language-local-name="Lets" 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 – Malagassisch" lang="mg" hreflang="mg" data-title="Aljebra" data-language-autonym="Malagasy" data-language-local-name="Malagassisch" 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 – Minangkabau" lang="min" hreflang="min" data-title="Aljabar" data-language-autonym="Minangkabau" data-language-local-name="Minangkabau" 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 – Macedonisch" lang="mk" hreflang="mk" data-title="Алгебра" data-language-autonym="Македонски" data-language-local-name="Macedonisch" 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 – Malayalam" lang="ml" hreflang="ml" data-title="ബീജഗണിതം" data-language-autonym="മലയാളം" data-language-local-name="Malayalam" 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 – Marathi" lang="mr" hreflang="mr" data-title="बीजगणित" data-language-autonym="मराठी" data-language-local-name="Marathi" 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 – Maleis" lang="ms" hreflang="ms" data-title="Algebra" data-language-autonym="Bahasa Melayu" data-language-local-name="Maleis" 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 – Maltees" lang="mt" hreflang="mt" data-title="Alġebra" data-language-autonym="Malti" data-language-local-name="Maltees" 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 – Mirandees" lang="mwl" hreflang="mwl" data-title="Álgebra" data-language-autonym="Mirandés" data-language-local-name="Mirandees" 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 – Birmaans" lang="my" hreflang="my" data-title="အက္ခရာသင်္ချာ" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="Birmaans" 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 – Nedersaksisch" lang="nds" hreflang="nds" data-title="Algebra" data-language-autonym="Plattdüütsch" data-language-local-name="Nedersaksisch" 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 – Nepalees" lang="ne" hreflang="ne" data-title="बिजगणित" data-language-autonym="नेपाली" data-language-local-name="Nepalees" 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 – Newari" lang="new" hreflang="new" data-title="बीजगणित" data-language-autonym="नेपाल भाषा" data-language-local-name="Newari" 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 – Nias" lang="nia" hreflang="nia" data-title="Aljabar" data-language-autonym="Li Niha" data-language-local-name="Nias" class="interlanguage-link-target"><span>Li Niha</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Algebra" title="Algebra – Noors - Nynorsk" lang="nn" hreflang="nn" data-title="Algebra" data-language-autonym="Norsk nynorsk" data-language-local-name="Noors - Nynorsk" 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 – Noors - Bokmål" lang="nb" hreflang="nb" data-title="Algebra" data-language-autonym="Norsk bokmål" data-language-local-name="Noors - Bokmål" 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 – Occitaans" lang="oc" hreflang="oc" data-title="Algèbra" data-language-autonym="Occitan" data-language-local-name="Occitaans" 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 – Afaan Oromo" lang="om" hreflang="om" data-title="Aljebraa" data-language-autonym="Oromoo" data-language-local-name="Afaan Oromo" 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 – Punjabi" lang="pa" hreflang="pa" data-title="ਅਲਜਬਰਾ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="Punjabi" 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 – Pools" lang="pl" hreflang="pl" data-title="Algebra" data-language-autonym="Polski" data-language-local-name="Pools" 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 – Piëmontees" lang="pms" hreflang="pms" data-title="Àlgebra" data-language-autonym="Piemontèis" data-language-local-name="Piëmontees" 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 – Pasjtoe" lang="ps" hreflang="ps" data-title="الجبر" data-language-autonym="پښتو" data-language-local-name="Pasjtoe" 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 – Portugees" lang="pt" hreflang="pt" data-title="Álgebra" data-language-autonym="Português" data-language-local-name="Portugees" 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 – Quechua" lang="qu" hreflang="qu" data-title="Qillqanancha kamay" data-language-autonym="Runa Simi" data-language-local-name="Quechua" 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 – Roemeens" lang="ro" hreflang="ro" data-title="Algebră" data-language-autonym="Română" data-language-local-name="Roemeens" 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 – Russisch" lang="ru" hreflang="ru" data-title="Алгебра" data-language-autonym="Русский" data-language-local-name="Russisch" 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 – Roetheens" lang="rue" hreflang="rue" data-title="Алґебра" data-language-autonym="Русиньскый" data-language-local-name="Roetheens" 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 – Jakoets" lang="sah" hreflang="sah" data-title="Алгебра" data-language-autonym="Саха тыла" data-language-local-name="Jakoets" 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 – Siciliaans" lang="scn" hreflang="scn" data-title="Àlgibbra" data-language-autonym="Sicilianu" data-language-local-name="Siciliaans" 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 – Schots" lang="sco" hreflang="sco" data-title="Algebra" data-language-autonym="Scots" data-language-local-name="Schots" 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 – Sindhi" lang="sd" hreflang="sd" data-title="آلجبرا" data-language-autonym="سنڌي" data-language-local-name="Sindhi" 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 – Servo-Kroatisch" lang="sh" hreflang="sh" data-title="Algebra" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Servo-Kroatisch" 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 – Tashelhiyt" lang="shi" hreflang="shi" data-title="Aljibr" data-language-autonym="Taclḥit" data-language-local-name="Tashelhiyt" 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 – Singalees" lang="si" hreflang="si" data-title="වීජ ගණිතය" data-language-autonym="සිංහල" data-language-local-name="Singalees" 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) – Slowaaks" lang="sk" hreflang="sk" data-title="Algebra (disciplína)" data-language-autonym="Slovenčina" data-language-local-name="Slowaaks" 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 – Sloveens" lang="sl" hreflang="sl" data-title="Algebra" data-language-autonym="Slovenščina" data-language-local-name="Sloveens" 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 – Somalisch" lang="so" hreflang="so" data-title="Aljebra" data-language-autonym="Soomaaliga" data-language-local-name="Somalisch" 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 – Albanees" lang="sq" hreflang="sq" data-title="Algjebra" data-language-autonym="Shqip" data-language-local-name="Albanees" 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 – Servisch" lang="sr" hreflang="sr" data-title="Алгебра" data-language-autonym="Српски / srpski" data-language-local-name="Servisch" 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 – Soendanees" lang="su" hreflang="su" data-title="Aljabar" data-language-autonym="Sunda" data-language-local-name="Soendanees" 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 – Zweeds" lang="sv" hreflang="sv" data-title="Algebra" data-language-autonym="Svenska" data-language-local-name="Zweeds" 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 – Swahili" lang="sw" hreflang="sw" data-title="Aljebra" data-language-autonym="Kiswahili" data-language-local-name="Swahili" 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 – Tamil" lang="ta" hreflang="ta" data-title="இயற்கணிதம்" data-language-autonym="தமிழ்" data-language-local-name="Tamil" 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 – Telugu" lang="te" hreflang="te" data-title="బీజ గణితం" data-language-autonym="తెలుగు" data-language-local-name="Telugu" 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 – Tadzjieks" lang="tg" hreflang="tg" data-title="Алгебра" data-language-autonym="Тоҷикӣ" data-language-local-name="Tadzjieks" 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 – Thai" lang="th" hreflang="th" data-title="พีชคณิต" data-language-autonym="ไทย" data-language-local-name="Thai" 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 – Turkmeens" lang="tk" hreflang="tk" data-title="Algebra" data-language-autonym="Türkmençe" data-language-local-name="Turkmeens" 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 – Turks" lang="tr" hreflang="tr" data-title="Cebir" data-language-autonym="Türkçe" data-language-local-name="Turks" 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 – Tsonga" lang="ts" hreflang="ts" data-title="Tinhlayo-swiyenge" data-language-autonym="Xitsonga" data-language-local-name="Tsonga" 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 – Tataars" lang="tt" hreflang="tt" data-title="Алгебра" data-language-autonym="Татарча / tatarça" data-language-local-name="Tataars" 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 – Toemboeka" lang="tum" hreflang="tum" data-title="Alijebra" data-language-autonym="ChiTumbuka" data-language-local-name="Toemboeka" 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 – Oekraïens" lang="uk" hreflang="uk" data-title="Алгебра" data-language-autonym="Українська" data-language-local-name="Oekraïens" 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 – Urdu" lang="ur" hreflang="ur" data-title="الجبرا" data-language-autonym="اردو" data-language-local-name="Urdu" 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 – Oezbeeks" lang="uz" hreflang="uz" data-title="Algebra" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Oezbeeks" 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 – Venetiaans" lang="vec" hreflang="vec" data-title="Àlgebra" data-language-autonym="Vèneto" data-language-local-name="Venetiaans" 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 – Wepsisch" lang="vep" hreflang="vep" data-title="Algebr" data-language-autonym="Vepsän kel’" data-language-local-name="Wepsisch" class="interlanguage-link-target"><span>Vepsän kel’</span></a></li><li class="interlanguage-link interwiki-vi badge-Q17437796 badge-featuredarticle mw-list-item" title="uitgelicht artikel"><a href="https://vi.wikipedia.org/wiki/%C4%90%E1%BA%A1i_s%E1%BB%91" title="Đại số – Vietnamees" lang="vi" hreflang="vi" data-title="Đại số" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamees" 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-Vlaams" lang="vls" hreflang="vls" data-title="Algebra" data-language-autonym="West-Vlams" data-language-local-name="West-Vlaams" 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 – Waray" lang="war" hreflang="war" data-title="Alhebra" data-language-autonym="Winaray" data-language-local-name="Waray" 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 – Wuyu" lang="wuu" hreflang="wuu" data-title="代数" data-language-autonym="吴语" data-language-local-name="Wuyu" 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 – Xhosa" lang="xh" hreflang="xh" data-title="I-Algebra" data-language-autonym="IsiXhosa" data-language-local-name="Xhosa" 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 – Mingreels" lang="xmf" hreflang="xmf" data-title="ალგებრა" data-language-autonym="მარგალური" data-language-local-name="Mingreels" 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 – Jiddisch" lang="yi" hreflang="yi" data-title="אלגעברע" data-language-autonym="ייִדיש" data-language-local-name="Jiddisch" 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 – Yoruba" lang="yo" hreflang="yo" data-title="Algebra" 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class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">Uit Wikipedia, de vrije encyclopedie</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="nl" dir="ltr"><div id="sjabloon_zie" class="hatnote" style="padding:0.5em; margin-bottom:0.5em; border-bottom:1px solid #aaa; font-size:95%;" role="note"><span style="padding-right:0.5em;"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ea/Disambig-dark.svg/25px-Disambig-dark.svg.png" decoding="async" width="25" height="19" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ea/Disambig-dark.svg/38px-Disambig-dark.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/ea/Disambig-dark.svg/50px-Disambig-dark.svg.png 2x" data-file-width="444" data-file-height="340" /></span></span></span> <i>Zie <a href="/wiki/Algebra_(doorverwijspagina)" class="mw-disambig" title="Algebra (doorverwijspagina)">Algebra (doorverwijspagina)</a> voor andere betekenissen van Algebra.</i> </div> <style data-mw-deduplicate="TemplateStyles:r67813444/mw-parser-output/.tmulti">.mw-parser-output .tmulti .multiimageinner{display:flex;flex-direction:column}.mw-parser-output .tmulti .trow{display:flex;flex-direction:row;clear:left;flex-wrap:wrap;width:100%;box-sizing:border-box}.mw-parser-output .tmulti .tsingle{margin:1px;float:left}.mw-parser-output .tmulti .theader{clear:both;font-weight:bold;text-align:center;align-self:center;background-color:transparent;width:100%}.mw-parser-output .tmulti .thumbcaption{background-color:transparent}.mw-parser-output .tmulti .text-align-left{text-align:left}.mw-parser-output .tmulti .text-align-right{text-align:right}.mw-parser-output .tmulti .text-align-center{text-align:center}@media all and (max-width:640px){.mw-parser-output .tmulti .tright{margin:unset}.mw-parser-output .tmulti .thumbinner{width:100%!important;box-sizing:border-box;max-width:none!important;align-items:center}.mw-parser-output .tmulti .trow{justify-content:center}.mw-parser-output .tmulti .tsingle{float:none!important;max-width:100%!important;box-sizing:border-box;text-align:center}.mw-parser-output .tmulti .tsingle .thumbcaption{text-align:left}.mw-parser-output .tmulti .trow>.thumbcaption{text-align:center}}</style><div class="thumb tmulti tright"><div class="thumbinner multiimageinner" style="width:317px;max-width:317px"><div class="trow"><div class="tsingle" style="width:315px;max-width:315px"><div class="thumbimage" style="height:58px;overflow:hidden"><span typeof="mw:File"><a href="/wiki/Polynoom" title="Polynoom"><img alt="Vergelijking van een polynoom" src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5b/Polynomial2.svg/313px-Polynomial2.svg.png" decoding="async" width="313" height="59" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5b/Polynomial2.svg/470px-Polynomial2.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5b/Polynomial2.svg/626px-Polynomial2.svg.png 2x" data-file-width="512" data-file-height="96" /></a></span></div><div class="thumbcaption"><a href="/wiki/Elementaire_algebra" title="Elementaire algebra">Elementaire algebra</a> richt zich op het oplossen van concrete vergelijkingen met behulp van rekenkundige bewerkingen.</div></div></div><div class="trow"><div class="tsingle" style="width:315px;max-width:315px"><div class="thumbimage" style="height:58px;overflow:hidden"><span typeof="mw:File"><a href="/wiki/Ring_of_integers" title="Ring of integers"><img alt="Signature of the ring of integers" src="//upload.wikimedia.org/wikipedia/commons/thumb/0/07/Ring_of_integers2.svg/313px-Ring_of_integers2.svg.png" decoding="async" width="313" height="59" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/07/Ring_of_integers2.svg/470px-Ring_of_integers2.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/07/Ring_of_integers2.svg/626px-Ring_of_integers2.svg.png 2x" data-file-width="512" data-file-height="96" /></a></span></div><div class="thumbcaption"><a href="/wiki/Abstracte_algebra" title="Abstracte algebra">Abstracte algebra</a> bestudeert <a href="/wiki/Algebra%C3%AFsche_structuur" title="Algebraïsche structuur">algebraïsche structuren</a>, zoals de <a href="/wiki/Ring_van_de_gehele_getallen" title="Ring van de gehele getallen">ring van de gehele getallen</a>: de verzameling <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 \mathbb {Z} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {Z} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/449494a083e0a1fda2b61c62b2f09b6bee4633dc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.55ex; height:2.176ex;" alt="{\displaystyle \mathbb {Z} }" /></span> uitgerust met <a href="/wiki/Operatie_(wiskunde)" title="Operatie (wiskunde)">operaties</a> van optelling (<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>) en vermenigvuldiging (<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>).</div></div></div></div></div> <table class="infobox" cellpadding="1" cellspacing="1"> <tbody><tr> <th class="infobox-kop notheme" colspan="3"><style data-mw-deduplicate="TemplateStyles:r56498100">.mw-parser-output .nobold{font-weight:normal}</style><span class="nobold">Deel van een <a href="/wiki/Categorie:Wiskunde" title="Categorie:Wiskunde">serie</a> artikelen over</span><br /><big><big>Wiskunde</big></big> </th></tr> <tr> <td class="ta-center" colspan="3"><span class="notpageimage" typeof="mw:File"><a href="/wiki/Bestand:CMAP_-_Centre_de_Math%C3%A9matiques_Appliqu%C3%A9es_de_l%27Ecole_polytechnique_(25911635211).jpg" class="mw-file-description" title="Formules van een stochastisch proces"><img alt="Formules van een stochastisch proces" src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d5/CMAP_-_Centre_de_Math%C3%A9matiques_Appliqu%C3%A9es_de_l%27Ecole_polytechnique_%2825911635211%29.jpg/264px-CMAP_-_Centre_de_Math%C3%A9matiques_Appliqu%C3%A9es_de_l%27Ecole_polytechnique_%2825911635211%29.jpg" decoding="async" width="264" height="176" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d5/CMAP_-_Centre_de_Math%C3%A9matiques_Appliqu%C3%A9es_de_l%27Ecole_polytechnique_%2825911635211%29.jpg/396px-CMAP_-_Centre_de_Math%C3%A9matiques_Appliqu%C3%A9es_de_l%27Ecole_polytechnique_%2825911635211%29.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d5/CMAP_-_Centre_de_Math%C3%A9matiques_Appliqu%C3%A9es_de_l%27Ecole_polytechnique_%2825911635211%29.jpg/528px-CMAP_-_Centre_de_Math%C3%A9matiques_Appliqu%C3%A9es_de_l%27Ecole_polytechnique_%2825911635211%29.jpg 2x" data-file-width="4724" data-file-height="3150" /></a></span> </td></tr> <tr> <td class="ta-center" colspan="3"><small>Formules van een <a href="/wiki/Stochastisch_proces" title="Stochastisch proces">stochastisch proces</a></small> </td></tr> <tr> <th class="infobox-kop notheme" colspan="3">Kwantiteit </th></tr> <tr> <td class="ta-center" colspan="3"> <p><a href="/wiki/Complex_getal" title="Complex getal">Complex getal</a> · <a href="/wiki/Geheel_getal" title="Geheel getal">Geheel getal</a> · <a href="/wiki/Natuurlijk_getal" title="Natuurlijk getal">Natuurlijk getal</a> · <a href="/wiki/Oneindigheid" title="Oneindigheid">Oneindigheid</a> · <a href="/wiki/Re%C3%ABel_getal" title="Reëel getal">Reëel getal</a> · <a href="/wiki/Rekenen" title="Rekenen">Rekenkunde</a> </p> </td></tr> <tr> <th class="infobox-kop notheme" colspan="3">Structuur en ruimte </th></tr> <tr> <td class="ta-center" colspan="3"> <p><a class="mw-selflink selflink">Algebra</a> · <a href="/wiki/Functie_(wiskunde)" title="Functie (wiskunde)">Functie</a> · <a href="/wiki/Getaltheorie" title="Getaltheorie">Getaltheorie</a> · <a href="/wiki/Goniometrie" title="Goniometrie">Goniometrie</a> · <a href="/wiki/Groepentheorie" title="Groepentheorie">Groepentheorie</a> · <a href="/wiki/Meetkunde" title="Meetkunde">Meetkunde</a> · <a href="/wiki/Topologie" title="Topologie">Topologie</a> </p> </td></tr> <tr> <th class="infobox-kop notheme" colspan="3">Verandering </th></tr> <tr> <td class="ta-center" colspan="3"> <p><a href="/wiki/Analyse_(wiskunde)" title="Analyse (wiskunde)">Analyse</a> · <a href="/wiki/Chaostheorie" title="Chaostheorie">Chaostheorie</a> · <a href="/wiki/Differentiaalrekening" title="Differentiaalrekening">Differentiaalrekening</a> · <a href="/wiki/Dynamisch_systeem" title="Dynamisch systeem">Dynamische systemen</a> · <a href="/wiki/Vectoranalyse" title="Vectoranalyse">Vectoren</a> </p> </td></tr> <tr> <th class="infobox-kop notheme" colspan="3">Toegepaste wiskunde </th></tr> <tr> <td class="ta-center" colspan="3"> <p><a href="/wiki/Discrete_wiskunde" title="Discrete wiskunde">Discrete wiskunde</a> · <a href="/wiki/Grafentheorie" title="Grafentheorie">Grafentheorie</a> · <a href="/wiki/Informatietheorie" title="Informatietheorie">Informatietheorie</a> · <a href="/wiki/Kansrekening" title="Kansrekening">Kansrekening</a> · <a href="/wiki/Statistiek" title="Statistiek">Statistiek</a> · <a href="/wiki/Wiskundige_natuurkunde" title="Wiskundige natuurkunde">Wiskundige natuurkunde</a> </p> </td></tr> <tr> <td class="infobox-kop center notheme" colspan="3"> <table cellspacing="0" cellpadding="0"> <tbody><tr> <td style="vertical-align:middle;"><b>Portaal</b>  <span class="noviewer" typeof="mw:File"><a href="/wiki/Bestand:Portal.svg" class="mw-file-description" title="Portaalicoon"><img alt="Portaalicoon" src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c9/Portal.svg/22px-Portal.svg.png" decoding="async" width="22" height="20" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c9/Portal.svg/33px-Portal.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c9/Portal.svg/44px-Portal.svg.png 2x" data-file-width="36" data-file-height="32" /></a></span>   </td> <td class="ta-left"><b><a href="/wiki/Portaal:Wiskunde" title="Portaal:Wiskunde">Wiskunde</a> </b> </td></tr></tbody></table> </td></tr> </tbody></table> <p><b>Algebra</b> is een tak van de <a href="/wiki/Wiskunde" title="Wiskunde">wiskunde</a> die zich richt op het werken met <a href="/wiki/Lijst_van_wiskundige_symbolen" title="Lijst van wiskundige symbolen">symbolen</a> en <a href="/wiki/Vergelijking_(wiskunde)" title="Vergelijking (wiskunde)">vergelijkingen</a> om problemen op te lossen. In plaats van alleen met <a href="/wiki/Getal_(wiskunde)" title="Getal (wiskunde)">getallen</a> te rekenen (<a href="/wiki/Rekenkunde" class="mw-redirect" title="Rekenkunde">rekenkunde</a>), maakt algebra gebruik van variabelen zoals <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}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle x}" /></span> en <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}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b8a6208ec717213d4317e666f1ae872e00620a0d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.155ex; height:2.009ex;" alt="{\displaystyle y}" /></span>. Deze variabelen vertegenwoordigen onbekende waarden, en kunnen met elkaar samenhangen in formules. </p><p><a href="/wiki/Elementaire_algebra" title="Elementaire algebra">Elementaire algebra</a> is de bekendste vorm van algebra die op scholen wordt onderwezen. Een belangrijk doel in elementaire algebra is het vinden van verbanden tussen variabelen en het oplossen van vergelijkingen. In de vergelijking <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 2x+3=7}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>2</mn> <mi>x</mi> <mo>+</mo> <mn>3</mn> <mo>=</mo> <mn>7</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 2x+3=7}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9f62ca8c5456ad58ab2fb8f4a03dc50510bdf84b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:10.756ex; height:2.343ex;" alt="{\displaystyle 2x+3=7}" /></span> kan men bijvoorbeeld de waarde van <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}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle x}" /></span> uitrekenen door een aantal algebraïsche stappen te volgen. <a href="/wiki/Lineaire_algebra" title="Lineaire algebra">Lineaire algebra</a> is een nauw verwant deelgebied dat zich bezighoudt met het oplossen van <a href="/wiki/Lineaire_vergelijking" title="Lineaire vergelijking">lineaire vergelijkingen</a> en <a href="/wiki/Stelsel_van_lineaire_vergelijkingen" title="Stelsel van lineaire vergelijkingen">stelsels</a>, wat onder meer relevant is voor de beschrijving van <a href="/wiki/Vector_(wiskunde)" title="Vector (wiskunde)">vectoren</a>. </p><p><a href="/wiki/Abstracte_algebra" title="Abstracte algebra">Abstracte algebra</a> gaat nog een stap verder, en bestudeert <a href="/wiki/Algebra%C3%AFsche_structuur" title="Algebraïsche structuur">algebraïsche structuren</a>, zoals <a href="/wiki/Groep_(wiskunde)" title="Groep (wiskunde)">groepen</a>, <a href="/wiki/Ring_(wiskunde)" title="Ring (wiskunde)">ringen</a> en <a href="/wiki/Veld_(wiskunde)" class="mw-redirect" title="Veld (wiskunde)">velden</a> en de regels waarmee deze zijn te beschrijven. Het is een generalisatie van de elementaire algebra, en wordt gebruikt als basis voor bijvoorbeeld <a href="/wiki/Algebra%C3%AFsche_meetkunde" title="Algebraïsche meetkunde">algebraïsche meetkunde</a> en <a href="/wiki/Algebra%C3%AFsche_getaltheorie" title="Algebraïsche getaltheorie">algebraïsche getaltheorie</a>. Algebra speelt een cruciale rol in het doorgronden van patronen, het modelleren van situaties uit de echte wereld en het maken van voorspellingen. Het wordt toegepast in veel vakgebieden, zoals <a href="/wiki/Wetenschap" title="Wetenschap">wetenschap</a>, <a href="/wiki/Techniek" title="Techniek">techniek</a>, <a href="/wiki/Logica" title="Logica">logica</a>, <a href="/wiki/Economie" title="Economie">economie</a> en <a href="/wiki/Informatica" title="Informatica">informatica</a>. </p><p>Algebraïsche methoden werden voor het eerst toegepast in de oudheid, veelal om concrete <a href="/wiki/Meetkunde" title="Meetkunde">meetkundige</a> problemen op te lossen. Wiskundige redeneringen werden later in de geschiedenis steeds ingewikkelder, waarvoor een strakker systeem van symbolen nodig was. Halverwege de 19e eeuw breidde de reikwijdte van algebra zich uit naar de theorie van complexere algebraïsche bewerkingen. De basisprincipes van algebra – zoals het werken met termen, vergelijkingen en formules – vormen de fundamenten voor meer geavanceerde onderwerpen in de wiskunde. Hierbij is te denken aan <a href="/wiki/Topologie" title="Topologie">topologie</a>, <a href="/wiki/Differentiaal-_en_integraalrekening" class="mw-redirect" title="Differentiaal- en integraalrekening">differentiaal- en integraalrekening</a> en <a href="/wiki/Wiskundige_logica" title="Wiskundige logica">wiskundige logica</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Etymologie">Etymologie</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Algebra&veaction=edit&section=1" title="Bewerk dit kopje: Etymologie" class="mw-editsection-visualeditor"><span>bewerken</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Algebra&action=edit&section=1" title="De broncode bewerken van de sectie: Etymologie"><span>brontekst bewerken</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-left" typeof="mw:File/Thumb"><a href="/wiki/Bestand:Image-Al-Kit%C4%81b_al-mu%E1%B8%ABta%E1%B9%A3ar_f%C4%AB_%E1%B8%A5is%C4%81b_al-%C4%9Fabr_wa-l-muq%C4%81bala.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/23/Image-Al-Kit%C4%81b_al-mu%E1%B8%ABta%E1%B9%A3ar_f%C4%AB_%E1%B8%A5is%C4%81b_al-%C4%9Fabr_wa-l-muq%C4%81bala.jpg/150px-Image-Al-Kit%C4%81b_al-mu%E1%B8%ABta%E1%B9%A3ar_f%C4%AB_%E1%B8%A5is%C4%81b_al-%C4%9Fabr_wa-l-muq%C4%81bala.jpg" decoding="async" width="150" height="238" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/23/Image-Al-Kit%C4%81b_al-mu%E1%B8%ABta%E1%B9%A3ar_f%C4%AB_%E1%B8%A5is%C4%81b_al-%C4%9Fabr_wa-l-muq%C4%81bala.jpg/225px-Image-Al-Kit%C4%81b_al-mu%E1%B8%ABta%E1%B9%A3ar_f%C4%AB_%E1%B8%A5is%C4%81b_al-%C4%9Fabr_wa-l-muq%C4%81bala.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/2/23/Image-Al-Kit%C4%81b_al-mu%E1%B8%ABta%E1%B9%A3ar_f%C4%AB_%E1%B8%A5is%C4%81b_al-%C4%9Fabr_wa-l-muq%C4%81bala.jpg 2x" data-file-width="240" data-file-height="380" /></a><figcaption>Een bladzijde uit het boek <i>al-djabr</i></figcaption></figure> <p>Omstreeks het jaar 820 schreef de Perzische wiskundige <a href="/wiki/Al-Chwarizmi" title="Al-Chwarizmi">Al-Chwarizmi</a> in het <a href="/wiki/Arabisch" title="Arabisch">Arabisch</a> een boek over het rekenen met letters: <i>hisab al-djabr wa al-muqabala</i> (Arabisch: حساب الجبر و المقابلة). Het woord <i>al-djabr</i> uit de titel van dat boek betekent hereniging, verbinding of vervollediging en gaf aanleiding tot het algemene gebruik van het woord algebra in het Westen. </p><p>Het Nederlandse woord 'stelkunde' dat <a href="/wiki/Simon_Stevin" title="Simon Stevin">Simon Stevin</a> probeerde in te voeren, werd nooit helemaal aanvaard. </p> <div class="mw-heading mw-heading2"><h2 id="Afbakening">Afbakening</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Algebra&veaction=edit&section=2" title="Bewerk dit kopje: Afbakening" class="mw-editsection-visualeditor"><span>bewerken</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Algebra&action=edit&section=2" title="De broncode bewerken van de sectie: Afbakening"><span>brontekst bewerken</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Oorspronkelijk was algebra een veralgemening van de <a href="/wiki/Rekenen" title="Rekenen">rekenkunde</a> waarin letters de rol van getallen overnamen. Rond 1800 bestond algebra uit het gebruik van letters om "de verbeelding te bevrijden" (<a href="/wiki/Gottfried_Wilhelm_Leibniz" title="Gottfried Wilhelm Leibniz">Gottfried Wilhelm Leibniz</a>) bij het uitvoeren van rekenkundige bewerkingen en het oplossen van <a href="/wiki/Vergelijking_(wiskunde)" title="Vergelijking (wiskunde)">vergelijkingen</a>.<sup id="cite_ref-derbyshire_1-0" class="reference"><a href="#cite_note-derbyshire-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p><p>In de loop van de 19de eeuw maakte de algebra zich los van de rechtstreekse band met getallen en rekenkunde, en werden abstracte structuren gedefinieerd aan de hand van enkele elementaire eigenschappen van de bekende getallenverzamelingen: <a href="/wiki/Groep_(wiskunde)" title="Groep (wiskunde)">groepen</a>, <a href="/wiki/Ring_(wiskunde)" title="Ring (wiskunde)">ringen</a>, <a href="/wiki/Lichaam_(Ned)_/_Veld_(Be)" title="Lichaam (Ned) / Veld (Be)">lichamen</a> en <a href="/wiki/Vectorruimte" title="Vectorruimte">vectorruimten</a>. De algebra onderging een wiskundige revolutie die erin bestond dat ze zich verwijderde van het rekenwerk en zich ging toespitsen op het onderscheiden en benutten van de structurele basis van de wiskunde.<sup id="cite_ref-tabak_2-0" class="reference"><a href="#cite_note-tabak-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p><p>Men onderscheidt thans ook een dergelijke abstracte structuur die <i>een</i> <a href="/wiki/Algebra_(structuur)" title="Algebra (structuur)">algebra</a> heet, en die bestaat uit een vectorruimte uitgerust met een vermenigvuldiging van vectoren. </p> <div class="mw-heading mw-heading2"><h2 id="Deelgebieden">Deelgebieden</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Algebra&veaction=edit&section=3" title="Bewerk dit kopje: Deelgebieden" class="mw-editsection-visualeditor"><span>bewerken</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Algebra&action=edit&section=3" title="De broncode bewerken van de sectie: Deelgebieden"><span>brontekst bewerken</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Op grond van de hierboven aangehaalde historische evolutie onderscheidt men meestal twee 'niveaus' in de algebra: </p> <ul><li><i>Elementaire algebra</i></li> <li><i>Abstracte algebra</i></li></ul> <p>Daarnaast hebben zich in sommige toepassingsgebieden van de wiskunde afzonderlijke onderzoeksdomeinen ontwikkeld die een welbepaalde toepassing van de elementaire of de abstracte algebra inhouden: </p> <ul><li><i><a href="/wiki/Financi%C3%ABle_algebra" class="mw-redirect" title="Financiële algebra">Financiële algebra</a></i>: bestudeert de algebra die zich met geld, beleggingen, rekeningen en dergelijke financiële zaken bezighoudt.</li> <li><i><a href="/wiki/Computeralgebra" class="mw-redirect" title="Computeralgebra">Computeralgebra</a></i>: bestudeert <a href="/wiki/Algoritme" title="Algoritme">algoritmen</a> voor de symbolische manipulatie van <a href="/wiki/Wiskundig_object" class="mw-redirect" title="Wiskundig object">wiskundige objecten</a>.</li></ul> <div class="mw-heading mw-heading3"><h3 id="Elementaire_algebra">Elementaire algebra</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Algebra&veaction=edit&section=4" title="Bewerk dit kopje: Elementaire algebra" class="mw-editsection-visualeditor"><span>bewerken</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Algebra&action=edit&section=4" title="De broncode bewerken van de sectie: Elementaire algebra"><span>brontekst bewerken</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><i>Zie <a href="/wiki/Elementaire_algebra" title="Elementaire algebra">Elementaire algebra</a> voor het hoofdartikel over dit onderwerp.</i> </p><p>De elementaire algebra bestudeert de eigenschappen van rekenkundige bewerkingen waarbij letters worden gebruikt om numerieke <a href="/wiki/Constante_(algebra)" class="mw-redirect" title="Constante (algebra)">constanten</a> en <a href="/wiki/Variabele" title="Variabele">variabelen</a> aan te duiden. Ook de regels die gelden voor uitdrukkingen en vergelijkingen met deze symbolen, worden bestudeerd. </p><p>In eerste instantie vormt de algebra een ondersteuning van het <a href="/wiki/Hoofdrekenen" title="Hoofdrekenen">hoofdrekenen</a>, een belangrijke praktische vaardigheid in het precomputertijdperk. Door het gebruik van letters kunnen algemene formules worden beschreven waarin men dan naar believen geschikte getallen kan invullen om een berekening eenvoudiger te maken. In dit verband nemen de <a href="/wiki/Merkwaardig_product" class="mw-redirect" title="Merkwaardig product">merkwaardige producten</a> een bijzondere plaats in; zo kan bijvoorbeeld het <a href="/wiki/Kwadraat" title="Kwadraat">kwadraat</a> van een getal van 2 cijfers worden uitgerekend door het getal te splitsen in tientallen en eenheden: </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 (10T+E)^{2}=100T^{2}+20TE+E^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mn>10</mn> <mi>T</mi> <mo>+</mo> <mi>E</mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mn>100</mn> <msup> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mn>20</mn> <mi>T</mi> <mi>E</mi> <mo>+</mo> <msup> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (10T+E)^{2}=100T^{2}+20TE+E^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5efcc7eaff022918a322e6d85e01e0f4e01e3856" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:35.066ex; height:3.176ex;" alt="{\displaystyle (10T+E)^{2}=100T^{2}+20TE+E^{2}}" /></span></dd></dl> <p>waarvoor men alleen de <a href="/wiki/Tafels_van_vermenigvuldiging" title="Tafels van vermenigvuldiging">tafels van vermenigvuldiging</a> tot <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 10\times 10}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>10</mn> <mo>×</mo> <mn>10</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 10\times 10}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/13637e2f9858def2b80ac81e3228b7f31df8b751" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.49ex; height:2.176ex;" alt="{\displaystyle 10\times 10}" /></span> hoeft uit het hoofd te kennen. </p><p>De belangrijkste toepassing van elementaire algebra ligt evenwel in het oplossen van <a href="/wiki/Vergelijking_(wiskunde)" title="Vergelijking (wiskunde)">vergelijkingen</a>. In een <a href="/wiki/Algebra%C3%AFsche_vergelijking" class="mw-redirect" title="Algebraïsche vergelijking">algebraïsche vergelijking</a> worden twee uitdrukkingen aan elkaar gelijkgesteld waarin alleen getallen, lettersymbolen en de vier rekenkundige <a href="/wiki/Operator_(wiskunde)" title="Operator (wiskunde)">hoofdbewerkingen</a> (met eventuele haakjes) voorkomen; door toepassing van elementaire rekenregels kan een algebraïsche vergelijking altijd worden herschreven als de voorwaarde dat een <a href="/wiki/Polynoom" title="Polynoom">polynoom</a> gelijk is aan 0. Het oplossen van een vergelijking is het vinden van de precieze verzameling getallen die in de lettersymbolen kunnen worden ingevuld opdat de gelijkheid zou voldaan zijn, de zogenaamde <i>nulpuntsverzameling</i> van het polynoom. </p><p>Algemener kan men een stelsel van meer vergelijkingen bestuderen; de oplossingsverzameling is dan de <a href="/wiki/Doorsnede_(verzamelingenleer)" title="Doorsnede (verzamelingenleer)">doorsnede</a> van de oplossingsverzamelingen van de afzonderlijke vergelijkingen. </p><p>Sommige vergelijkingen of stelsels kunnen met elementaire middelen worden opgelost, zoals de <a href="/wiki/Lineaire_vergelijking" title="Lineaire vergelijking">lineaire vergelijking</a> en de <a href="/wiki/Vierkantsvergelijking" title="Vierkantsvergelijking">vierkantsvergelijking</a>; anderen hebben aanleiding gegeven tot geheel nieuwe onderzoeksdomeinen. De <a href="/wiki/Meetkunde" title="Meetkunde">meetkundige</a> voorstelling van de oplossingsverzameling van een stelsel algebraïsche vergelijkigen is de <a href="/wiki/Algebra%C3%AFsche_meetkunde" title="Algebraïsche meetkunde">algebraïsche meetkunde</a>. De <a href="/wiki/Lineaire_algebra" title="Lineaire algebra">lineaire algebra</a> is ontstaan uit de studie van <a href="/wiki/Stelsel_van_lineaire_vergelijkingen" title="Stelsel van lineaire vergelijkingen">stelsels van lineaire vergelijkingen</a>. </p><p>De oplossingsverzameling van een vergelijking wordt meestal <i>a priori</i> beperkt tot een getallenverzameling die de auteur van het probleem als aanvaardbaar beschouwt. Of een vergelijking oplosbaar is, hangt natuurlijk sterk af van die keuze: de vergelijking <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+1=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mo>+</mo> <mn>1</mn> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x+1=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6408d831afc1e1cfcfd45d47b7d3b7bdfbee036f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:9.593ex; height:2.343ex;" alt="{\displaystyle x+1=0}" /></span> heeft geen oplossingen voor <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}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle x}" /></span> binnen de verzameling <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 \mathbb {N} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">N</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {N} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fdf9a96b565ea202d0f4322e9195613fb26a9bed" 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 \mathbb {N} }" /></span> der <a href="/wiki/Natuurlijk_getal" title="Natuurlijk getal">natuurlijke getallen</a>, maar wel binnen de <a href="/wiki/Geheel_getal" title="Geheel getal">gehele</a> of de <a href="/wiki/Rationaal_getal" title="Rationaal getal">rationale getallen</a>. </p><p>Historisch is vaak het omgekeerde gebeurd: omdat een bepaalde vergelijking geen oplossing had, hebben mensen de verzameling der "aanvaardbare" getallen kunstmatig uitgebreid. De uitvinding van negatieve getallen is een dergelijke kunstgreep om alle vergelijkingen met optellingen zoals <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+1=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mo>+</mo> <mn>1</mn> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x+1=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6408d831afc1e1cfcfd45d47b7d3b7bdfbee036f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:9.593ex; height:2.343ex;" alt="{\displaystyle x+1=0}" /></span> oplosbaar te maken. Breuken zijn een uitbreiding van de gehele getallen om vergelijkingen zoals <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 3x=2}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>3</mn> <mi>x</mi> <mo>=</mo> <mn>2</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 3x=2}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cbbdb3bba613f0cf1da99b13f02addd83c1a7d01" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.753ex; height:2.176ex;" alt="{\displaystyle 3x=2}" /></span> op te lossen. De <a href="/wiki/Complex_getal" title="Complex getal">complexe getallen</a> bieden en oplossing voor <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^{2}+1=0,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mn>1</mn> <mo>=</mo> <mn>0</mn> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x^{2}+1=0,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6eefe27838566005bb9c66404d2d74ae699f9b72" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:11.295ex; height:3.009ex;" alt="{\displaystyle x^{2}+1=0,}" /></span> en het symbool <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 {\sqrt {a}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mi>a</mi> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\sqrt {a}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/afccc332c876539296df1a980127d86173e59ef0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.166ex; height:3.009ex;" alt="{\displaystyle {\sqrt {a}}}" /></span> voor de <a href="/wiki/Vierkantswortel" title="Vierkantswortel">vierkantswortel</a> betekent niets anders dan "de (of een) oplossing van de vergelijking <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^{2}=a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x^{2}=a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d5860855b0ebfad26053afeaea0748e40c9ce070" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.712ex; height:2.676ex;" alt="{\displaystyle x^{2}=a}" /></span>". </p><p>Een <a href="/wiki/Diofantische_vergelijking" title="Diofantische vergelijking">diofantische vergelijking</a> is een algebraïsche vergelijking waarbij men eist dat de oplossingen gehele getallen zijn. De <a href="/wiki/Getaltheorie" title="Getaltheorie">getaltheorie</a> is ontstaan uit de studie van diofantische vergelijkingen. </p> <div class="mw-heading mw-heading3"><h3 id="Abstracte_algebra">Abstracte algebra</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Algebra&veaction=edit&section=5" title="Bewerk dit kopje: Abstracte algebra" class="mw-editsection-visualeditor"><span>bewerken</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Algebra&action=edit&section=5" title="De broncode bewerken van de sectie: Abstracte algebra"><span>brontekst bewerken</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><i>Zie <a href="/wiki/Abstracte_algebra" title="Abstracte algebra">Abstracte algebra</a> voor het hoofdartikel over dit onderwerp.</i> </p><p>De abstracte algebra bestudeert <a href="/wiki/Algebra%C3%AFsche_structuur" title="Algebraïsche structuur">algebraïsche structuren</a> zoals lichamen, groepen en ringen. De <i>lineaire algebra,</i> die <a href="/wiki/Vectorruimte" title="Vectorruimte">vectorruimten</a> en bijbehorende <a href="/wiki/Lineaire_transformatie" title="Lineaire transformatie">lineaire transformaties</a> bestudeert, kan worden opgevat als onderdeel hiervan maar bekleedt toch een eigen plaats door het grote aantal rechtstreekse toepassingen buiten de wiskunde. </p><p>De abstracte algebra staat niet los van de elementaire algebra, maar is eruit ontstaan omdat abstracte structuren een cruciaal nieuw inzicht verschaften in moeilijke elementaire problemen. </p><p>De <i><a href="/wiki/Groepentheorie" title="Groepentheorie">groepentheorie</a></i> bestudeert abstracte bewerkingen, <a href="/wiki/Groep_(wiskunde)" title="Groep (wiskunde)">groepsbewerkingen</a> genaamd, die de volgende eigenschappen gemeen hebben met de <a href="/wiki/Optellen" title="Optellen">optelling</a> van gehele getallen: </p> <ul><li><a href="/wiki/Associativiteit_(wiskunde)" title="Associativiteit (wiskunde)">associativiteit</a>: bij het samenstellen van een element met het resultaat van de samenstelling van twee andere elementen, hangt het eindresultaat niet af van de plaatsing van de haakjes;</li> <li><a href="/wiki/Neutraal_element" title="Neutraal element">neutraal element</a>: er bestaat een element dat, samengesteld met eender welk ander element, als resultaat dat andere element oplevert;</li> <li><a href="/wiki/Inverse_element" title="Inverse element">inversen</a>: voor ieder element bestaat een ander element dat ermee samengesteld het neutraal element oplevert.</li></ul> <p>Men spreekt van een commutatieve of <a href="/wiki/Abelse_groep" title="Abelse groep">abelse groep</a> als bovendien het resultaat niet afhangt van de volgorde der elementen. </p><p>Groepen zijn de zuiverste <a href="/wiki/Abstractie" title="Abstractie">abstractie</a> van het begrip <a href="/wiki/Symmetrie" title="Symmetrie">symmetrie</a>. </p><p>De <i><a href="/wiki/Ringtheorie" title="Ringtheorie">ringtheorie</a></i> kijkt naar combinaties van twee bewerkingen, op een abstract niveau vergelijkbaar met de optelling en de vermenigvuldiging van gehele getallen of de optelling en vermenigvuldiging van <a href="/wiki/Polynoom" title="Polynoom">veeltermen</a>. De eerste bewerking vormt een abelse groep, terwijl de tweede bewerking er in een bepaalde zin compatibel mee moet zijn (<a href="/wiki/Distributiviteit" title="Distributiviteit">distributiviteit</a>). </p><p>Bij een <i><a href="/wiki/Lichaam_(Ned)_/_Veld_(Be)" title="Lichaam (Ned) / Veld (Be)">lichaam</a></i> wordt ook de omkeerbaarheid van de vermenigvuldiging geëist; dit naar analogie met het rekenen in de rationale, reële of complexe getallen. De <a href="/wiki/Galoistheorie" title="Galoistheorie">Galoistheorie</a> bestudeert de bijzondere relatie tussen een lichaam en zijn deellichamen aan de hand van groepentheorie. </p><p>In de lineaire algebra is een <i>vectorruimte</i> een abstractie van de coördinatenruimte waarin meetkunde wordt bedreven; ze bestaat enerzijds uit een lichaam waarvan de elementen "<a href="/wiki/Scalair" title="Scalair">scalair</a>en" heten (naar analogie met de <a href="/wiki/Re%C3%ABel_getal" title="Reëel getal">reële getallen</a>), en anderzijds uit "vectoren" die bij elkaar kunnen worden opgeteld en die met een scalair kunnen worden vermenigvuldigd. </p><p>Van deze vier basisstructuren zijn inmiddels tientallen varianten, specialisaties en veralgemeningen beschreven, die allemaal specifieke toepassingen hebben voor het oplossen van problemen uit de elementaire algebra of uit andere takken van de wiskunde. Het reeds aangehaalde artikel <i><a href="/wiki/Algebra%C3%AFsche_structuur" title="Algebraïsche structuur">Algebraïsche structuur</a></i> somt er nog enkele op. </p><p>Tussen twee objecten van dezelfde <a href="/wiki/Categorie_(wiskunde)" title="Categorie (wiskunde)">categorie</a> (bijvoorbeeld twee groepen) onderscheidt men <a href="/wiki/Morfisme" title="Morfisme">morfismen</a>: <a href="/wiki/Afbeelding_(wiskunde)" title="Afbeelding (wiskunde)">afbeeldingen</a> tussen de abstracte verzamelingen die de bewerkingsstructuur respecteren. Een <a href="/wiki/Groepshomomorfisme" title="Groepshomomorfisme">groepshomomorfisme</a> tussen twee groepen <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,\cdot )}"> <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,\cdot )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1ccc71a6904c5ab99ecaab1c8ed69e20815d66da" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.317ex; height:2.843ex;" alt="{\displaystyle (G,\cdot )}" /></span> en <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 (H,*)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>H</mi> <mo>,</mo> <mo>∗</mo> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (H,*)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1ca9efa8f60b1acd949386d15ff163c637042933" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.069ex; height:2.843ex;" alt="{\displaystyle (H,*)}" /></span> is een afbeelding tussen de onderliggende verzamelingen <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:G\to H:g\mapsto f(g)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo>:</mo> <mi>G</mi> <mo stretchy="false">→</mo> <mi>H</mi> <mo>:</mo> <mi>g</mi> <mo stretchy="false">↦</mo> <mi>f</mi> <mo stretchy="false">(</mo> <mi>g</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f:G\to H:g\mapsto f(g)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e9607fd9f3f3fef71cc0847af70195e0407e42af" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:21.591ex; height:2.843ex;" alt="{\displaystyle f:G\to H:g\mapsto f(g)}" /></span> die als volgt de groepsbewerking bewaart: </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 \forall g_{1},g_{2}\in G:f(g_{1}\cdot g_{2})=f(g_{1})*f(g_{2})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∀</mi> <msub> <mi>g</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>g</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>∈</mo> <mi>G</mi> <mo>:</mo> <mi>f</mi> <mo stretchy="false">(</mo> <msub> <mi>g</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>⋅</mo> <msub> <mi>g</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">)</mo> <mo>=</mo> <mi>f</mi> <mo stretchy="false">(</mo> <msub> <mi>g</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo stretchy="false">)</mo> <mo>∗</mo> <mi>f</mi> <mo stretchy="false">(</mo> <msub> <mi>g</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \forall g_{1},g_{2}\in G:f(g_{1}\cdot g_{2})=f(g_{1})*f(g_{2})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/72da2428f5337b0d3ba1ed645a9451f97293c7ad" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:38.147ex; height:2.843ex;" alt="{\displaystyle \forall g_{1},g_{2}\in G:f(g_{1}\cdot g_{2})=f(g_{1})*f(g_{2})}" /></span></dd></dl> <p>Een omkeerbaar morfisme heet <a href="/wiki/Isomorfisme" title="Isomorfisme">isomorfisme</a>. Als tussen twee objecten (verzamelingen met een bewerking) een isomorfisme bestaat, zijn ze in algebraïsch opzicht volkomen gelijkwaardig. </p><p>Een typisch probleem van de abstracte algebra bestaat erin, de objecten van een gegeven categorie te classificeren op isomorfisme na. Een van de merkwaardigste resultaten van de 20ste-eeuwse algebra is de <a href="/wiki/Classificatie_van_eindige_enkelvoudige_groepen" title="Classificatie van eindige enkelvoudige groepen">classificatie van eindige enkelvoudige groepen</a>. </p><p>De <a href="/wiki/Homologische_algebra" title="Homologische algebra">homologische algebra</a> bestudeert niet één specifieke categorie van structuren, maar algemene <a href="/wiki/Ketencomplex" title="Ketencomplex">ketencomplexen</a> waarvan de objecten tot tamelijk algemene categorieën kunnen behoren; ze is ontstaan uit de behoefte om technieken van de <a href="/wiki/Algebra%C3%AFsche_topologie" title="Algebraïsche topologie">algebraïsche topologie</a> aan te wenden bij de studie van objecten die niet <i>a priori</i> met topologie te maken hebben. </p> <div class="toccolours appendix" role="presentation" style="font-size:90%; margin:1em 0 -0.5em; clear:both;"> <div><span style="font-weight:bold">Bronnen, noten en/of referenties</span></div> <div class="reflist" style="list-style-type: decimal;"><div class="mw-references-wrap"><ol class="references"> <li id="cite_note-derbyshire-1"><span class="mw-cite-backlink"><a href="#cite_ref-derbyshire_1-0">↑</a></span> <span class="reference-text">Inleiding tot Derbyshire, John, "Unknown Quantity - A Real and Imaginary History of Algebra," Joseph Henry Press 2006.</span> </li> <li id="cite_note-tabak-2"><span class="mw-cite-backlink"><a href="#cite_ref-tabak_2-0">↑</a></span> <span class="reference-text">Hoofdstuk 6 "The Search for New Structures" in Tabak, John, "Algebra - Sets, Symbols, and the Language of Thought," Facts on File 2004.</span> </li> </ol></div></div> </div> <style data-mw-deduplicate="TemplateStyles:r67837862">.mw-parser-output .navigatie{position:relative;clear:both;overflow:auto;margin:1em auto -0.5em;padding:2px;background-color:var(--background-color-neutral-subtle,#f8f9fa);border:1px solid 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