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rootpage-Category_Ideal_ring_theory skin-vector action-view"><div id="mw-page-base" class="noprint"></div> <div id="mw-head-base" class="noprint"></div> <div id="content" class="mw-body" role="main"> <a id="top"></a> <div id="siteNotice"></div> <div class="mw-indicators"> <div id="mw-indicator-mw-helplink" class="mw-indicator"><a href="/wiki/Commons:Categories" target="_blank" class="mw-helplink"><span class="mw-helplink-icon"></span>Help</a></div> </div> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-namespace">Category</span><span class="mw-page-title-separator">:</span><span class="mw-page-title-main">Ideal (ring theory)</span></h1> <div id="bodyContent" class="vector-body"> <div id="siteSub" class="noprint">From Wikimedia Commons, the free media repository</div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="contentSub2"></div> <div id="jump-to-nav"></div> <a class="mw-jump-link" href="#mw-head">Jump to navigation</a> <a class="mw-jump-link" href="#searchInput">Jump to search</a> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><style data-mw-deduplicate="TemplateStyles:r905765184">.mw-parser-output #wdinfobox[dir="ltr"]{float:right;clear:right;margin-right:0;margin-left:1em}.mw-parser-output #wdinfobox[dir="rtl"]{float:left;clear:left;margin-left:0;margin-right:1em}.mw-parser-output #wdinfobox{width:258px;box-sizing:border-box;font-size:95%;padding:0}.mw-parser-output #wdinfobox .image img{max-width:250px;max-height:250px;width:auto}.mw-parser-output #wdinfoboxcaption{background:#FFF}.mw-parser-output #wdinfobox[dir="ltr"] #wdinfoboxcaption{margin-left:0}.mw-parser-output #wdinfobox[dir="rtl"] #wdinfoboxcaption{margin-right:0}.mw-parser-output #wdinfobox th,.mw-parser-output #wdinfo_taxon th{vertical-align:top;word-wrap:break-word;hyphens:auto}.mw-parser-output #wdinfobox td,.mw-parser-output #wdinfo_taxon td{word-wrap:break-word;hyphens:auto}.mw-parser-output #wdinfobox li:not(:last-child){margin-bottom:3px}.mw-parser-output #wdinfo_taxon{font-size:95%;table-layout:fixed;padding:0}.mw-parser-output .taxontree-lcell,.mw-parser-output .wikidatainfobox-lcell{background:#CFE3FF;padding-left:.4em;padding-right:.4em;font-weight:bold}.mw-parser-output .taxontree-rcell,.mw-parser-output .wikidatainfobox-rcell{word-wrap:break-word;hyphens:auto}.mw-parser-output #wdinfobox[dir="ltr"] .taxontree-lcell,.mw-parser-output #wdinfobox[dir="ltr"] .wikidatainfobox-lcell{text-align:right;word-wrap:break-word;hyphens:auto}.mw-parser-output #wdinfobox[dir="rtl"] .taxontree-lcell,.mw-parser-output #wdinfobox[dir="rtl"] .wikidatainfobox-lcell{text-align:left;word-wrap:break-word;hyphens:auto}.mw-parser-output .taxontree-fullcell{text-align:center}.mw-parser-output .taxontree-hdrcell{text-align:center;background:#CFE3FF;padding-left:.4em;padding-right:.4em;font-weight:bold}.mw-parser-output .taxontree-row{}@media screen and (max-width:600px){.mw-parser-output .wdinfo_nomobile{display:none;visibility:hidden;height:0}}.mw-parser-output .wdinfobox_horizontal{clear:both!important;display:block;box-sizing:border-box!important;width:100%!important;column-width:24em}.mw-parser-output .wdinfobox_hide{display:none}.mw-parser-output #wdcreator{display:none}.mw-parser-output .wdcreator_show{display:block!important}.mw-parser-output #wdinfo_taxon ul{list-style:none;list-style-position:inside}.mw-parser-output #wdinfobox[dir="ltr"] #wdinfo_taxon ul{padding-left:0;margin-left:0}.mw-parser-output #wdinfobox[dir="rtl"] #wdinfo_taxon ul{padding-right:0;margin-right:0}.mw-parser-output .wikidatainfoboxVN ul li{list-style:none;padding:0;margin:0}.mw-parser-output .wikidatainfoboxVN ul{margin-left:0}.mw-parser-output .wikidatainfoboxVN{padding:0;margin:0}</style><div style="display:none"><nowiki>ideal; 環倍數; 이데알; ideal; Ideal; Ideaal; ایده‌آل (نظریه حلقه‌ها); 理想; Ideal; ideal; イデアル; Ideal (theoria de anellos); Ideál; אידיאל; 環理想; 아이디얼; Идеал; idealo; ideál; வளையத்தில் சீர்மம்; ideale; idéal; Идеал (алгебра); Ideal; ideal; ideal; Ringi ideaal; ideal; Идеал; Идеал; ideal; идеал; ideal; ідеал; ideal; Ideal i matematikk; ideal; ideaal; Ideal; ideał; ideál; I-đê-an; ideal; مثالي; Ιδεώδες; Ideaali; subgrup aditiv al unui inel închis sub înmulțire cu un element oarecare al inelului; 環の特別な部分集合; ensemble d'un anneau stable par addition et par multiplication d'un de ses éléments avec un élément quelconque de l'anneau, intervenant dans la construction des anneaux quotients; számelméleti és topológiai fogalom; menggeneralisasi himpunan bagian tertentu dari bilangan bulat, seperti bilangan genap atau kelipatan 3; typ podzbioru pierścienia; מושג במתמטיקה; wiskunde; понятие в теории колец; subestructura algebraica; additive Untergruppe eines Ringes, die unter Multiplikation mit beliebigen Ringelementen abgeschlossen ist; subgrupo aditivo de um anel fechado sob a multiplicação por um elemento arbitrário do anel; subgrupo aditivo dun anel pechado baixo a multiplicación por calquera elemento arbitrario do anel; tia adicia subgrupo de ringo, ke multipliko de ĉiu ĝia elemento kaj ia ajn elemento de la ringo apartenas al ĝi; additive subgroup of a ring closed under multiplcation by arbitrary ring element; subgrupo aditivo de um anel fechado sob a multiplicação por um elemento arbitrário do anel; ideale di anello; イデヤル; 理想数; Vänsterideal; Högerideal; Maximalt ideal; Matematisk ideal; אידאל; теория идеалов; Linksideal; Rechtsideal; 좌 아이디얼; 우 아이디얼; 진 아이디얼; 양측 아이디얼; ideal de un anillo; ideal próprio; 环理想; 理想子环; 代数理想; 极大理想; 双边理想; ідеал кільця</nowiki></div><table id="wdinfobox" class="fileinfotpl-type-information vevent infobox mw-collapsible mw-content-ltr"><caption class="fn org" id="wdinfoboxcaption"><b>ideal </b></caption><tbody><tr><td colspan="2" class="wdinfo_nomobile" style="text-align:center"><div>additive subgroup of a ring closed under multiplcation by arbitrary ring element</div><div class="switcher-container"></div></td></tr><tr><td colspan="2" style="text-align:center"><b><a class="external text" href="https://commons.wikimedia.org/w/index.php?title=Special%3AUploadWizard&categories=Ideal+%28ring+theory%29">Upload media</a></b></td></tr><tr><td colspan="2" style="text-align:center; font-weight:bold"><div><span typeof="mw:File"><span><img alt="" src="https://upload.wikimedia.org/wikipedia/commons/thumb/8/80/Wikipedia-logo-v2.svg/16px-Wikipedia-logo-v2.svg.png" decoding="async" width="16" height="15" class="mw-file-element" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/8/80/Wikipedia-logo-v2.svg/24px-Wikipedia-logo-v2.svg.png 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/8/80/Wikipedia-logo-v2.svg/32px-Wikipedia-logo-v2.svg.png 2x" data-file-width="103" data-file-height="94" /></span></span> <a href="https://en.wikipedia.org/wiki/Ideal_(ring_theory)" class="extiw" title="en:Ideal (ring theory)">Wikipedia</a></div><div><span typeof="mw:File"><span><img alt="" src="https://upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikibooks-logo.svg/16px-Wikibooks-logo.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikibooks-logo.svg/24px-Wikibooks-logo.svg.png 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/f/fa/Wikibooks-logo.svg/32px-Wikibooks-logo.svg.png 2x" data-file-width="300" data-file-height="300" /></span></span> <a href="https://en.wikibooks.org/wiki/en:Abstract_Algebra/Ideals" class="extiw" title="b:en:Abstract Algebra/Ideals">Wikibooks</a></div></td></tr><tr class="wdinfo_nomobile"><th class="wikidatainfobox-lcell">Subclass of</th><td><div class="plainlist"><ul><li><a href="/wiki/Category:Abelian_groups" title="Category:Abelian groups">abelian group</a></li><li>rng</li><li>submodule</li></ul></div></td></tr><tr class="wdinfo_nomobile"><th class="wikidatainfobox-lcell">Part of</th><td><div class="plainlist"><ul><li>ring</li></ul></div></td></tr><tr class="wdinfo_nomobile"><th class="wikidatainfobox-lcell">Different from</th><td><div class="plainlist"><ul><li><a href="https://www.wikidata.org/wiki/Q1656686" class="extiw" title="d:Q1656686"><span title="in order theory, a nonempty, upward‐directed, downward‐closed subset of a preordered set">ideal</span></a></li><li><a href="https://www.wikidata.org/wiki/Q1497184" class="extiw" title="d:Q1497184"><span title="generalization of the ring-theoretical notion of ideal to integral domains">fractional ideal</span></a></li></ul></div></td></tr><tr><td colspan="2"><table style="width:100%" id="wdinfo_ac" class="mw-collapsible"><tbody><tr><th style="background: #cfe3ff">Authority file</th></tr><tr><td style="text-align: center;"><div style="overflow-wrap: break-word; font-size: smaller"><span typeof="mw:File"><a href="https://www.wikidata.org/wiki/Q44649" title="d:Q44649"><img alt="Wikidata" src="https://upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Wikidata-logo.svg/20px-Wikidata-logo.svg.png" decoding="async" width="20" height="11" class="mw-file-element" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Wikidata-logo.svg/30px-Wikidata-logo.svg.png 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Wikidata-logo.svg/40px-Wikidata-logo.svg.png 2x" data-file-width="1050" data-file-height="590" /></a></span> <a href="https://www.wikidata.org/wiki/Q44649" class="extiw" title="d:Q44649">Q44649</a><br /><span class="wdinfo_nomobile"><span typeof="mw:File"><span><img alt="" src="https://upload.wikimedia.org/wikipedia/commons/thumb/8/8e/Logo_Gemeinsame_Normdatei_%28GND%29.svg/18px-Logo_Gemeinsame_Normdatei_%28GND%29.svg.png" decoding="async" width="18" height="21" class="mw-file-element" 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https://upload.wikimedia.org/wikipedia/commons/thumb/9/9e/Library_of_Congress_favicon.png/36px-Library_of_Congress_favicon.png 2x" data-file-width="64" data-file-height="64" /></span></span> Library of Congress authority ID: <span><span><a rel="nofollow" class="external text" href="https://id.loc.gov/authorities/sh85064134">sh85064134</a></span></span><br /><span typeof="mw:File"><span><img alt="" src="https://upload.wikimedia.org/wikipedia/commons/thumb/8/84/Logo_BnF.svg/18px-Logo_BnF.svg.png" decoding="async" width="18" height="7" class="mw-file-element" srcset="https://upload.wikimedia.org/wikipedia/commons/thumb/8/84/Logo_BnF.svg/27px-Logo_BnF.svg.png 1.5x, https://upload.wikimedia.org/wikipedia/commons/thumb/8/84/Logo_BnF.svg/36px-Logo_BnF.svg.png 2x" data-file-width="677" data-file-height="252" /></span></span> Bibliothèque nationale de France ID: <span><span><a rel="nofollow" class="external text" href="https://catalogue.bnf.fr/ark:/12148/cb119794357">119794357</a></span></span><br />BabelNet ID: <span><span><a rel="nofollow" class="external text" href="https://babelnet.org/synset?id=bn:01952066n&lang=EN">01952066n</a></span></span><br />J9U ID: <span><span><a rel="nofollow" class="external text" href="http://olduli.nli.org.il/F/?func=find-b&local_base=NLX10&find_code=UID&request=987007538412305171">987007538412305171</a></span></span></span></div></td></tr><tr class="wdinfo_nomobile"><td colspan="2" style="text-align: center"><small><div class="hlist hlist-separated"><ul><li><span style="white-space:nowrap"><a class="external text" href="https://reasonator.toolforge.org/?q=Q44649">Reasonator</a></span></li><li><span style="white-space:nowrap"><a href="https://iw.toolforge.org/scholia/Q44649" class="extiw" title="toolforge:scholia/Q44649">Scholia</a></span></li><li><span style="white-space:nowrap"><a rel="nofollow" class="external text" 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class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Ideal_(matem%C3%A0tiques)" title="Ideal (matemàtiques) – Catalan" lang="ca" hreflang="ca" data-title="Ideal (matemàtiques)" data-language-autonym="Català" data-language-local-name="Catalan" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Ide%C3%A1l_(teorie_okruh%C5%AF)" title="Ideál (teorie okruhů) – Czech" lang="cs" hreflang="cs" data-title="Ideál (teorie okruhů)" data-language-autonym="Čeština" data-language-local-name="Czech" 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%98%D0%B4%D0%B5%D0%B0%D0%BB_(%D0%B0%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0)" title="Идеал (алгебра) – Chuvash" lang="cv" hreflang="cv" data-title="Идеал (алгебра)" data-language-autonym="Чӑвашла" 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Greek" lang="el" hreflang="el" data-title="Ιδεώδες (μαθηματικά)" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Ideal_(ring_theory)" title="Ideal (ring theory) – English" lang="en" hreflang="en" data-title="Ideal (ring theory)" data-language-autonym="English" data-language-local-name="English" 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/Idealo_(algebro)" title="Idealo (algebro) – Esperanto" lang="eo" hreflang="eo" data-title="Idealo (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/Ideal_(teor%C3%ADa_de_anillos)" title="Ideal (teoría de anillos) – Spanish" lang="es" hreflang="es" data-title="Ideal (teoría de anillos)" data-language-autonym="Español" data-language-local-name="Spanish" 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/Ringi_ideaal" title="Ringi ideaal – Estonian" lang="et" hreflang="et" data-title="Ringi ideaal" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%A7%DB%8C%D8%AF%D9%87%E2%80%8C%D8%A2%D9%84_(%D9%86%D8%B8%D8%B1%DB%8C%D9%87_%D8%AD%D9%84%D9%82%D9%87%E2%80%8C%D9%87%D8%A7)" title="ایده‌آل (نظریه حلقه‌ها) – Persian" lang="fa" hreflang="fa" data-title="ایده‌آل (نظریه حلقه‌ها)" data-language-autonym="فارسی" data-language-local-name="Persian" 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/Ideaali_(rengasteoria)" title="Ideaali (rengasteoria) – Finnish" lang="fi" hreflang="fi" data-title="Ideaali (rengasteoria)" data-language-autonym="Suomi" data-language-local-name="Finnish" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Id%C3%A9al" title="Idéal – French" lang="fr" hreflang="fr" data-title="Idéal" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Ideal_(teor%C3%ADa_dos_aneis)" title="Ideal (teoría dos aneis) – Galician" lang="gl" hreflang="gl" data-title="Ideal (teoría dos aneis)" data-language-autonym="Galego" data-language-local-name="Galician" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%90%D7%99%D7%93%D7%99%D7%90%D7%9C_(%D7%90%D7%9C%D7%92%D7%91%D7%A8%D7%94)" title="אידיאל (אלגברה) – Hebrew" lang="he" hreflang="he" data-title="אידיאל (אלגברה)" data-language-autonym="עברית" data-language-local-name="Hebrew" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Ide%C3%A1l_(gy%C5%B1r%C5%B1elm%C3%A9let)" title="Ideál (gyűrűelmélet) – Hungarian" lang="hu" hreflang="hu" data-title="Ideál (gyűrűelmélet)" data-language-autonym="Magyar" data-language-local-name="Hungarian" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Ideal_(theoria_de_anellos)" title="Ideal (theoria de anellos) – Interlingua" lang="ia" hreflang="ia" data-title="Ideal (theoria de anellos)" data-language-autonym="Interlingua" data-language-local-name="Interlingua" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Ideal_(teori_gelanggang)" title="Ideal (teori gelanggang) – Indonesian" lang="id" hreflang="id" data-title="Ideal (teori gelanggang)" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesian" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Ideale_(matematica)" title="Ideale (matematica) – Italian" lang="it" hreflang="it" data-title="Ideale (matematica)" data-language-autonym="Italiano" data-language-local-name="Italian" 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/%E3%82%A4%E3%83%87%E3%82%A2%E3%83%AB_(%E7%92%B0%E8%AB%96)" title="イデアル (環論) – Japanese" lang="ja" hreflang="ja" data-title="イデアル (環論)" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%98%D0%B4%D0%B5%D0%B0%D0%BB_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0%D0%B4%D0%B0)" title="Идеал (математикада) – Kazakh" lang="kk" hreflang="kk" data-title="Идеал (математикада)" data-language-autonym="Қазақша" data-language-local-name="Kazakh" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%95%84%EC%9D%B4%EB%94%94%EC%96%BC" title="아이디얼 – Korean" lang="ko" hreflang="ko" data-title="아이디얼" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-lmo mw-list-item"><a href="https://lmo.wikipedia.org/wiki/Ideaal_(matem%C3%A0tica)" title="Ideaal (matemàtica) – Lombard" lang="lmo" hreflang="lmo" data-title="Ideaal (matemàtica)" data-language-autonym="Lombard" data-language-local-name="Lombard" class="interlanguage-link-target"><span>Lombard</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Ideaal_(ringtheorie)" title="Ideaal (ringtheorie) – Dutch" lang="nl" hreflang="nl" data-title="Ideaal (ringtheorie)" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Ideal_i_matematikk" title="Ideal i matematikk – Norwegian Nynorsk" lang="nn" hreflang="nn" data-title="Ideal i matematikk" data-language-autonym="Norsk nynorsk" data-language-local-name="Norwegian 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/Ideal_(matematikk)" title="Ideal (matematikk) – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Ideal (matematikk)" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Idea%C5%82_(teoria_pier%C5%9Bcieni)" title="Ideał (teoria pierścieni) – Polish" lang="pl" hreflang="pl" data-title="Ideał (teoria pierścieni)" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Ideal_(teoria_dos_an%C3%A9is)" title="Ideal (teoria dos anéis) – Portuguese" lang="pt" hreflang="pt" data-title="Ideal (teoria dos anéis)" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Ideal_(teoria_inelelor)" title="Ideal (teoria inelelor) – Romanian" lang="ro" hreflang="ro" data-title="Ideal (teoria inelelor)" data-language-autonym="Română" data-language-local-name="Romanian" 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%98%D0%B4%D0%B5%D0%B0%D0%BB_(%D0%B0%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0)" title="Идеал (алгебра) – Russian" lang="ru" hreflang="ru" data-title="Идеал (алгебра)" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Ide%C3%A1l_(okruhu)" title="Ideál (okruhu) – Slovak" lang="sk" hreflang="sk" data-title="Ideál (okruhu)" data-language-autonym="Slovenčina" data-language-local-name="Slovak" 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/Ideal_(teorija_kolobarjev)" title="Ideal (teorija kolobarjev) – Slovenian" lang="sl" hreflang="sl" data-title="Ideal (teorija kolobarjev)" data-language-autonym="Slovenščina" data-language-local-name="Slovenian" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%98%D0%B4%D0%B5%D0%B0%D0%BB_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)" title="Идеал (математика) – Serbian" lang="sr" hreflang="sr" data-title="Идеал (математика)" data-language-autonym="Српски / srpski" data-language-local-name="Serbian" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Ideal_(ringteori)" title="Ideal (ringteori) – Swedish" lang="sv" hreflang="sv" data-title="Ideal (ringteori)" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%B5%E0%AE%B3%E0%AF%88%E0%AE%AF%E0%AE%A4%E0%AF%8D%E0%AE%A4%E0%AE%BF%E0%AE%B2%E0%AF%8D_%E0%AE%9A%E0%AF%80%E0%AE%B0%E0%AF%8D%E0%AE%AE%E0%AE%AE%E0%AF%8D_(%E0%AE%95%E0%AE%A3%E0%AE%BF%E0%AE%A4%E0%AE%AE%E0%AF%8D)" title="வளையத்தில் சீர்மம் (கணிதம்) – Tamil" lang="ta" hreflang="ta" data-title="வளையத்தில் சீர்மம் (கணிதம்)" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%86%D0%B4%D0%B5%D0%B0%D0%BB_(%D0%B0%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0)" title="Ідеал (алгебра) – Ukrainian" lang="uk" hreflang="uk" data-title="Ідеал (алгебра)" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/I-%C4%91%C3%AA-an" title="I-đê-an – Vietnamese" lang="vi" hreflang="vi" data-title="I-đê-an" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnamese" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E7%92%B0%E5%80%8D%E6%95%B8" title="環倍數 – Cantonese" lang="yue" hreflang="yue" data-title="環倍數" data-language-autonym="粵語" data-language-local-name="Cantonese" class="interlanguage-link-target"><span>粵語</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E7%90%86%E6%83%B3_(%E7%8E%AF%E8%AE%BA)" title="理想 (环论) – Chinese" lang="zh" hreflang="zh" data-title="理想 (环论)" data-language-autonym="中文" data-language-local-name="Chinese" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a 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