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id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="サイト"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-namespace">Template</span><span class="mw-page-title-separator">:</span><span class="mw-page-title-main">代数的構造</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="特定の記事の別の言語版に移動します。 利用可能な言語14件" > <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-14" 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">14の言語版</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%82%D8%A7%D9%84%D8%A8:%D8%A8%D9%86%D9%8A%D8%A7%D8%AA_%D8%AC%D8%A8%D8%B1%D9%8A%D8%A9" title="アラビア語: قالب:بنيات جبرية" lang="ar" hreflang="ar" data-title="قالب:بنيات جبرية" data-language-autonym="العربية" data-language-local-name="アラビア語" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Template:Algebraic_structures" title="英語: Template:Algebraic structures" lang="en" hreflang="en" data-title="Template:Algebraic structures" data-language-autonym="English" data-language-local-name="英語" 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/%C5%9Cablono:Algebraj_strukturoj" title="エスペラント語: Ŝablono:Algebraj strukturoj" lang="eo" hreflang="eo" data-title="Ŝablono:Algebraj strukturoj" data-language-autonym="Esperanto" data-language-local-name="エスペラント語" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%A7%D9%84%DA%AF%D9%88:%D8%B3%D8%A7%D8%AE%D8%AA%D8%A7%D8%B1%D9%87%D8%A7%DB%8C_%D8%AC%D8%A8%D8%B1%DB%8C" title="ペルシア語: الگو:ساختارهای جبری" lang="fa" hreflang="fa" data-title="الگو:ساختارهای جبری" data-language-autonym="فارسی" data-language-local-name="ペルシア語" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Mod%C3%A8le:Palette_Structures_alg%C3%A9briques" title="フランス語: Modèle:Palette Structures algébriques" lang="fr" hreflang="fr" data-title="Modèle:Palette Structures algébriques" data-language-autonym="Français" data-language-local-name="フランス語" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%B8%E0%A4%BE%E0%A4%81%E0%A4%9A%E0%A4%BE:%E0%A4%AC%E0%A5%80%E0%A4%9C%E0%A4%97%E0%A4%A3%E0%A4%BF%E0%A4%A4%E0%A4%BF%E0%A4%AF_%E0%A4%B8%E0%A4%82%E0%A4%B0%E0%A4%9A%E0%A4%A8%E0%A4%BE" title="ヒンディー語: साँचा:बीजगणितिय संरचना" lang="hi" hreflang="hi" data-title="साँचा:बीजगणितिय संरचना" data-language-autonym="हिन्दी" data-language-local-name="ヒンディー語" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Templat:Struktur_aljabar" title="インドネシア語: Templat:Struktur aljabar" lang="id" hreflang="id" data-title="Templat:Struktur aljabar" data-language-autonym="Bahasa Indonesia" data-language-local-name="インドネシア語" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%ED%8B%80:%EB%8C%80%EC%88%98_%EA%B5%AC%EC%A1%B0" title="韓国語: 틀:대수 구조" lang="ko" hreflang="ko" data-title="틀:대수 구조" data-language-autonym="한국어" data-language-local-name="韓国語" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Sjabloon:Zijbalk_algebra%C3%AFsche_structuren" title="オランダ語: Sjabloon:Zijbalk algebraïsche structuren" lang="nl" hreflang="nl" data-title="Sjabloon:Zijbalk algebraïsche structuren" data-language-autonym="Nederlands" data-language-local-name="オランダ語" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Szablon:Struktury_algebraiczne" title="ポーランド語: Szablon:Struktury algebraiczne" lang="pl" hreflang="pl" data-title="Szablon:Struktury algebraiczne" data-language-autonym="Polski" data-language-local-name="ポーランド語" 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/Predefini%C3%A7%C3%A3o:Estruturas_alg%C3%A9bricas" title="ポルトガル語: Predefinição:Estruturas algébricas" lang="pt" hreflang="pt" data-title="Predefinição:Estruturas algébricas" data-language-autonym="Português" data-language-local-name="ポルトガル語" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A8%D0%B0%D0%B1%D0%BB%D0%BE%D0%BD:%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B8%D1%87%D0%BD%D1%96_%D1%81%D1%82%D1%80%D1%83%D0%BA%D1%82%D1%83%D1%80%D0%B8" title="ウクライナ語: Шаблон:Алгебричні структури" lang="uk" hreflang="uk" data-title="Шаблон:Алгебричні структури" data-language-autonym="Українська" data-language-local-name="ウクライナ語" 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/B%E1%BA%A3n_m%E1%BA%ABu:C%E1%BA%A5u_tr%C3%BAc_%C4%91%E1%BA%A1i_s%E1%BB%91" title="ベトナム語: Bản mẫu:Cấu trúc đại số" lang="vi" hreflang="vi" data-title="Bản mẫu:Cấu trúc đại số" data-language-autonym="Tiếng Việt" data-language-local-name="ベトナム語" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/Template:Algebraic_structures" title="中国語: Template:Algebraic structures" lang="zh" hreflang="zh" data-title="Template:Algebraic structures" data-language-autonym="中文" data-language-local-name="中国語" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q6675772#sitelinks-wikipedia" title="言語間リンクを編集" class="wbc-editpage">リンクを編集</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="名前空間"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-template" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Template:%E4%BB%A3%E6%95%B0%E7%9A%84%E6%A7%8B%E9%80%A0" title="テンプレートを表示 [c]" 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accesskey="h"><span>履歴表示</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="ページツール"> <div id="vector-page-tools-dropdown" class="vector-dropdown vector-page-tools-dropdown" > <input type="checkbox" id="vector-page-tools-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-tools-dropdown" class="vector-dropdown-checkbox " aria-label="ツール" > <label id="vector-page-tools-dropdown-label" for="vector-page-tools-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">ツール</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-tools-unpinned-container" class="vector-unpinned-container"> <div id="vector-page-tools" class="vector-page-tools vector-pinnable-element"> <div class="vector-pinnable-header vector-page-tools-pinnable-header vector-pinnable-header-unpinned" data-feature-name="page-tools-pinned" data-pinnable-element-id="vector-page-tools" data-pinned-container-id="vector-page-tools-pinned-container" data-unpinned-container-id="vector-page-tools-unpinned-container" > <div class="vector-pinnable-header-label">ツール</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">サイドバーに移動</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">非表示</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="その他の操作" > <div class="vector-menu-heading"> 操作 </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-more-view" class="selected vector-more-collapsible-item mw-list-item"><a href="/wiki/Template:%E4%BB%A3%E6%95%B0%E7%9A%84%E6%A7%8B%E9%80%A0"><span>閲覧</span></a></li><li id="ca-more-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Template:%E4%BB%A3%E6%95%B0%E7%9A%84%E6%A7%8B%E9%80%A0&action=edit" title="このページのソースコードを編集する [e]" accesskey="e"><span>ソースを編集</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=Template:%E4%BB%A3%E6%95%B0%E7%9A%84%E6%A7%8B%E9%80%A0&action=history"><span>履歴表示</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> 全般 </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/%E7%89%B9%E5%88%A5:%E3%83%AA%E3%83%B3%E3%82%AF%E5%85%83/Template:%E4%BB%A3%E6%95%B0%E7%9A%84%E6%A7%8B%E9%80%A0" title="ここにリンクしている全ウィキページの一覧 [j]" accesskey="j"><span>リンク元</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/%E7%89%B9%E5%88%A5:%E9%96%A2%E9%80%A3%E3%83%9A%E3%83%BC%E3%82%B8%E3%81%AE%E6%9B%B4%E6%96%B0%E7%8A%B6%E6%B3%81/Template:%E4%BB%A3%E6%95%B0%E7%9A%84%E6%A7%8B%E9%80%A0" rel="nofollow" title="このページからリンクしているページの最近の更新 [k]" accesskey="k"><span>関連ページの更新状況</span></a></li><li id="t-upload" class="mw-list-item"><a href="/wiki/Wikipedia:%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB%E3%81%AE%E3%82%A2%E3%83%83%E3%83%97%E3%83%AD%E3%83%BC%E3%83%89" title="ファイルをアップロードする [u]" accesskey="u"><span>ファイルをアップロード</span></a></li><li id="t-specialpages" class="mw-list-item"><a href="/wiki/%E7%89%B9%E5%88%A5:%E7%89%B9%E5%88%A5%E3%83%9A%E3%83%BC%E3%82%B8%E4%B8%80%E8%A6%A7" title="特別ページの一覧 [q]" accesskey="q"><span>特別ページ</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=Template:%E4%BB%A3%E6%95%B0%E7%9A%84%E6%A7%8B%E9%80%A0&oldid=98016849" title="このページのこの版への固定リンク"><span>この版への固定リンク</span></a></li><li id="t-info" 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.sidebar-above,.mw-parser-output .sidebar-below{padding:0.3em 0.8em;font-weight:bold}.mw-parser-output .sidebar-collapse .sidebar-above,.mw-parser-output .sidebar-collapse .sidebar-below{border-top:1px solid #aaa;border-bottom:1px solid #aaa}.mw-parser-output .sidebar-navbar{text-align:right;font-size:75%;padding:0 0.4em 0.4em}.mw-parser-output .sidebar-list-title{padding:0 0.4em;text-align:left;font-weight:bold;line-height:1.6em;font-size:105%}.mw-parser-output .sidebar-list-title-c{padding:0 0.4em;text-align:center;margin:0 3.3em}@media(max-width:720px){body.mediawiki .mw-parser-output .sidebar{width:100%!important;clear:both;float:none!important;margin-left:0!important;margin-right:0!important}}</style><table class="sidebar sidebar-collapse nomobile nowraplinks plainlist" style="width:20.0em;"><tbody><tr><th class="sidebar-title"><a href="/wiki/%E4%BB%A3%E6%95%B0%E7%9A%84%E6%A7%8B%E9%80%A0" title="代数的構造">代数的構造</a></th></tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="text-align:center;"><a href="/wiki/%E7%BE%A4_(%E6%95%B0%E5%AD%A6)" title="群 (数学)">群</a>に似た構造</div><div class="sidebar-list-content mw-collapsible-content"> <ul><li><a href="/wiki/%E7%BE%A4_(%E6%95%B0%E5%AD%A6)" title="群 (数学)">群</a></li> <li><a href="/wiki/%E5%8D%8A%E7%BE%A4" title="半群">半群</a> / <a href="/wiki/%E3%83%A2%E3%83%8E%E3%82%A4%E3%83%89" title="モノイド">モノイド</a></li> <li><a href="/wiki/%E5%9C%AD_(%E6%95%B0%E5%AD%A6)" title="圭 (数学)">圭</a></li> <li><a href="/wiki/%E6%BA%96%E7%BE%A4" title="準群">準群とループ</a></li></ul> <div class="hlist hlist-separated"> <ul><li><a href="/wiki/%E3%82%A2%E3%83%BC%E3%83%99%E3%83%AB%E7%BE%A4" title="アーベル群">アーベル群</a></li> <li><a href="/wiki/%E3%83%9E%E3%82%B0%E3%83%9E_(%E6%95%B0%E5%AD%A6)" title="マグマ (数学)">マグマ</a></li> <li><a href="/wiki/%E3%83%AA%E3%83%BC%E7%BE%A4" title="リー群">リー群</a></li></ul> </div> <a href="/wiki/%E7%BE%A4%E8%AB%96" title="群論">群論</a></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="text-align:center;"><a href="/wiki/%E7%92%B0_(%E6%95%B0%E5%AD%A6)" title="環 (数学)">環</a>に似た構造</div><div class="sidebar-list-content mw-collapsible-content"><div class="hlist hlist-separated"> <ul><li><a href="/wiki/%E7%92%B0_(%E6%95%B0%E5%AD%A6)" title="環 (数学)">環</a></li> <li><a href="/wiki/%E5%8D%8A%E7%92%B0" title="半環">半環</a></li> <li><span title="リンク先の項目はまだありません。新規の執筆や他言語版からの翻訳が望まれます。"><a href="/w/index.php?title=%E8%BF%91%E7%92%B0&action=edit&redlink=1" class="new" title="「近環」 (存在しないページ)">近環</a><span style="font-size: 0.77em; font-weight: normal;" class="noprint">(<a href="https://en.wikipedia.org/wiki/Near-ring" class="extiw" title="en:Near-ring">英語版</a>)</span></span></li> <li><a href="/wiki/%E5%8F%AF%E6%8F%9B%E7%92%B0" title="可換環">可換環</a></li> <li><a href="/wiki/%E6%95%B4%E5%9F%9F" title="整域">整域</a></li> <li><a href="/wiki/%E5%8F%AF%E6%8F%9B%E4%BD%93" title="可換体">体</a></li> <li><a href="/wiki/%E5%8F%AF%E9%99%A4%E7%92%B0" class="mw-redirect" title="可除環">可除環</a></li> <li><a href="/wiki/%E3%83%AA%E3%83%BC%E7%92%B0" class="mw-redirect" title="リー環">リー環</a></li></ul> </div> <a href="/wiki/%E7%92%B0%E8%AB%96" title="環論">環論</a></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="text-align:center;"><a href="/wiki/%E6%9D%9F_(%E6%9D%9F%E8%AB%96)" title="束 (束論)">束</a>に似た構造</div><div class="sidebar-list-content mw-collapsible-content"><div class="hlist hlist-separated"> <ul><li><a href="/wiki/%E6%9D%9F_(%E6%9D%9F%E8%AB%96)" title="束 (束論)">束</a></li> <li><a href="/wiki/%E6%9D%9F_(%E6%9D%9F%E8%AB%96)" title="束 (束論)">半束</a></li> <li><a href="/wiki/%E5%8F%AF%E8%A3%9C%E6%9D%9F" title="可補束">可補束</a></li> <li><a href="/wiki/%E5%85%A8%E9%A0%86%E5%BA%8F" title="全順序">全順序</a></li> <li><a href="/wiki/%E3%83%8F%E3%82%A4%E3%83%86%E3%82%A3%E3%83%B3%E3%82%B0%E4%BB%A3%E6%95%B0" title="ハイティング代数">ハイティング代数</a></li> <li><a href="/w/index.php?title=%E3%83%96%E3%83%BC%E3%83%AB%E4%BB%A3%E6%95%B0_(%E6%A7%8B%E9%80%A0)&action=edit&redlink=1" class="new" title="「ブール代数 (構造)」 (存在しないページ)">ブール代数</a></li></ul> </div> <ul><li><a href="https://en.wikipedia.org/wiki/Map_of_lattices" class="extiw" title="en:Map of lattices">en:Map of lattices</a></li> <li><a href="/wiki/%E6%9D%9F_(%E6%9D%9F%E8%AB%96)" title="束 (束論)">束論</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="text-align:center;"><a href="/wiki/%E7%92%B0%E4%B8%8A%E3%81%AE%E5%8A%A0%E7%BE%A4" title="環上の加群">加群</a>に似た構造</div><div class="sidebar-list-content mw-collapsible-content"><div class="hlist hlist-separated"> <ul><li><a href="/wiki/%E7%92%B0%E4%B8%8A%E3%81%AE%E5%8A%A0%E7%BE%A4" title="環上の加群">加群</a></li> <li><a href="/wiki/%E4%BD%9C%E7%94%A8%E3%82%92%E6%8C%81%E3%81%A4%E7%BE%A4" class="mw-redirect" title="作用を持つ群">作用を持つ群</a></li> <li><a href="/wiki/%E3%83%99%E3%82%AF%E3%83%88%E3%83%AB%E7%A9%BA%E9%96%93" title="ベクトル空間">ベクトル空間</a></li></ul> </div> <ul><li><a href="/wiki/%E7%B7%9A%E5%BD%A2%E4%BB%A3%E6%95%B0" class="mw-redirect" title="線形代数">線形代数</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible mw-collapsed"><div class="sidebar-list-title" style="text-align:center;"><a href="/wiki/%E4%BD%93%E4%B8%8A%E3%81%AE%E5%A4%9A%E5%85%83%E7%92%B0" title="体上の多元環">代数</a>に似た構造</div><div class="sidebar-list-content mw-collapsible-content"> <ul><li><a href="/wiki/%E4%BD%93%E4%B8%8A%E3%81%AE%E5%A4%9A%E5%85%83%E7%92%B0" title="体上の多元環">代数</a></li></ul> <div class="hlist hlist-separated"> <ul><li><a href="/wiki/%E7%B5%90%E5%90%88%E5%A4%9A%E5%85%83%E7%92%B0" title="結合多元環">結合</a></li> <li><a href="/wiki/%E5%88%86%E9%85%8D%E5%A4%9A%E5%85%83%E7%92%B0" title="分配多元環">非結合</a></li> <li><a href="/wiki/%E5%90%88%E6%88%90%E4%BB%A3%E6%95%B0" title="合成代数">合成代数</a></li></ul> <ul><li><a href="/wiki/%E3%83%AA%E3%83%BC%E4%BB%A3%E6%95%B0" title="リー代数">リー代数</a></li> <li><a href="/wiki/%E6%AC%A1%E6%95%B0%E4%BB%98%E3%81%8D%E7%92%B0" title="次数付き環">次数付き</a></li> <li><a href="/wiki/%E5%8F%8C%E4%BB%A3%E6%95%B0" title="双代数">双代数</a></li> <li><a href="/wiki/%E3%83%9B%E3%83%83%E3%83%97%E4%BB%A3%E6%95%B0" title="ホップ代数">ホップ代数</a></li></ul> </div></div></div></td> </tr><tr><td class="sidebar-navbar"><style data-mw-deduplicate="TemplateStyles:r99966302">.mw-parser-output .hlist ul,.mw-parser-output .hlist ol{padding-left:0}.mw-parser-output .hlist li,.mw-parser-output .hlist dd,.mw-parser-output .hlist dt{margin-right:0;display:inline-block;white-space:nowrap}.mw-parser-output .hlist dt:after,.mw-parser-output .hlist dd:after,.mw-parser-output .hlist li:after{white-space:normal}.mw-parser-output .hlist li:after,.mw-parser-output .hlist dd:after{content:" ·\a0 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