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class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="사이트"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="목차" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">목차</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">사이드바로 이동</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">숨기기</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">처음 위치</div> </a> </li> <li id="toc-성질" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#성질"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>성질</span> </div> </a> <ul id="toc-성질-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-아이젠슈타인_소수" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#아이젠슈타인_소수"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>아이젠슈타인 소수</span> </div> </a> <ul id="toc-아이젠슈타인_소수-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-외부_링크" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#외부_링크"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>외부 링크</span> </div> </a> <ul id="toc-외부_링크-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-같이_보기" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#같이_보기"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>같이 보기</span> </div> </a> <ul id="toc-같이_보기-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="목차" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="목차 토글" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">목차 토글</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">아이젠슈타인 정수</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="다른 언어로 문서를 방문합니다. 19개 언어로 읽을 수 있습니다" > <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-19" 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">19개 언어</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%B9%D8%AF%D8%AF_%D8%A3%D9%8A%D8%B2%D9%86%D8%B4%D8%AA%D8%A7%D9%8A%D9%86_%D8%A7%D9%84%D8%B5%D8%AD%D9%8A%D8%AD" title="عدد أيزنشتاين الصحيح – 아랍어" lang="ar" hreflang="ar" data-title="عدد أيزنشتاين الصحيح" data-language-autonym="العربية" data-language-local-name="아랍어" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Enter_d%27Eisenstein" title="Enter d'Eisenstein – 카탈로니아어" lang="ca" hreflang="ca" data-title="Enter d'Eisenstein" data-language-autonym="Català" data-language-local-name="카탈로니아어" 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/Eisensteinovo_%C4%8D%C3%ADslo" title="Eisensteinovo číslo – 체코어" lang="cs" hreflang="cs" data-title="Eisensteinovo číslo" data-language-autonym="Čeština" data-language-local-name="체코어" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Eisenstein-Zahl" title="Eisenstein-Zahl – 독일어" lang="de" hreflang="de" data-title="Eisenstein-Zahl" data-language-autonym="Deutsch" data-language-local-name="독일어" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Eisenstein_integer" title="Eisenstein integer – 영어" lang="en" hreflang="en" data-title="Eisenstein integer" data-language-autonym="English" data-language-local-name="영어" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Entero_de_Eisenstein" title="Entero de Eisenstein – 스페인어" lang="es" hreflang="es" data-title="Entero de Eisenstein" data-language-autonym="Español" data-language-local-name="스페인어" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Eisensteinin_kokonaisluku" title="Eisensteinin kokonaisluku – 핀란드어" lang="fi" hreflang="fi" data-title="Eisensteinin kokonaisluku" data-language-autonym="Suomi" data-language-local-name="핀란드어" 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/Entier_d%27Eisenstein" title="Entier d'Eisenstein – 프랑스어" lang="fr" hreflang="fr" data-title="Entier d'Eisenstein" data-language-autonym="Français" data-language-local-name="프랑스어" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%97%D7%95%D7%92_%D7%94%D7%A9%D7%9C%D7%9E%D7%99%D7%9D_%D7%A9%D7%9C_%D7%90%D7%99%D7%99%D7%96%D7%A0%D7%A9%D7%98%D7%99%D7%99%D7%9F" title="חוג השלמים של אייזנשטיין – 히브리어" lang="he" hreflang="he" data-title="חוג השלמים של אייזנשטיין" data-language-autonym="עברית" data-language-local-name="히브리어" 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/Eisenstein-eg%C3%A9sz" title="Eisenstein-egész – 헝가리어" lang="hu" hreflang="hu" data-title="Eisenstein-egész" data-language-autonym="Magyar" data-language-local-name="헝가리어" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Intero_di_Eisenstein" title="Intero di Eisenstein – 이탈리아어" lang="it" hreflang="it" data-title="Intero di Eisenstein" data-language-autonym="Italiano" data-language-local-name="이탈리아어" 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%A2%E3%82%A4%E3%82%BC%E3%83%B3%E3%82%B7%E3%83%A5%E3%82%BF%E3%82%A4%E3%83%B3%E6%95%B4%E6%95%B0" title="アイゼンシュタイン整数 – 일본어" lang="ja" hreflang="ja" data-title="アイゼンシュタイン整数" data-language-autonym="日本語" data-language-local-name="일본어" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%90%D1%98%D0%B7%D0%B5%D0%BD%D1%88%D1%82%D0%B0%D1%98%D0%BD%D0%BE%D0%B2_%D1%86%D0%B5%D0%BB_%D0%B1%D1%80%D0%BE%D1%98" title="Ајзенштајнов цел број – 마케도니아어" lang="mk" hreflang="mk" data-title="Ајзенштајнов цел број" data-language-autonym="Македонски" data-language-local-name="마케도니아어" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Geheel_getal_van_Eisenstein" title="Geheel getal van Eisenstein – 네덜란드어" lang="nl" hreflang="nl" data-title="Geheel getal van Eisenstein" data-language-autonym="Nederlands" data-language-local-name="네덜란드어" 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/Liczby_ca%C5%82kowite_Eisensteina" title="Liczby całkowite Eisensteina – 폴란드어" lang="pl" hreflang="pl" data-title="Liczby całkowite Eisensteina" data-language-autonym="Polski" data-language-local-name="폴란드어" 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/Inteiro_de_Eisenstein" title="Inteiro de Eisenstein – 포르투갈어" lang="pt" hreflang="pt" data-title="Inteiro de Eisenstein" data-language-autonym="Português" data-language-local-name="포르투갈어" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%A7%D0%B8%D1%81%D0%BB%D0%BE_%D0%AD%D0%B9%D0%B7%D0%B5%D0%BD%D1%88%D1%82%D0%B5%D0%B9%D0%BD%D0%B0" title="Число Эйзенштейна – 러시아어" lang="ru" hreflang="ru" data-title="Число Эйзенштейна" data-language-autonym="Русский" data-language-local-name="러시아어" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A6%D1%96%D0%BB%D0%B5_%D1%87%D0%B8%D1%81%D0%BB%D0%BE_%D0%95%D0%B9%D0%B7%D0%B5%D0%BD%D1%88%D1%82%D0%B5%D0%B9%D0%BD%D0%B0" title="Ціле число Ейзенштейна – 우크라이나어" lang="uk" hreflang="uk" data-title="Ціле число Ейзенштейна" data-language-autonym="Українська" data-language-local-name="우크라이나어" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E8%89%BE%E6%A3%AE%E6%96%AF%E5%9D%A6%E6%95%B4%E6%95%B0" title="艾森斯坦整数 – 중국어" lang="zh" hreflang="zh" data-title="艾森斯坦整数" data-language-autonym="中文" data-language-local-name="중국어" 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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class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="페이지 도구"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="보이기"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">보이기</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">사이드바로 이동</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">숨기기</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">위키백과, 우리 모두의 백과사전.</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="ko" dir="ltr"><p><span class="nowrap"></span> </p> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/%ED%8C%8C%EC%9D%BC:Eisenstein%27s_integer_numbers.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f7/Eisenstein%27s_integer_numbers.svg/408px-Eisenstein%27s_integer_numbers.svg.png" decoding="async" width="408" height="275" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f7/Eisenstein%27s_integer_numbers.svg/612px-Eisenstein%27s_integer_numbers.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f7/Eisenstein%27s_integer_numbers.svg/816px-Eisenstein%27s_integer_numbers.svg.png 2x" data-file-width="1632" data-file-height="1101" /></a><figcaption>아이젠슈타인 정수들은 복소평면에서 삼각 격자를 이룬다.</figcaption></figure> <p><a href="/wiki/%EC%88%98%EB%A1%A0" title="수론">수론</a>에서 <b>아이젠슈타인 정수</b>(<span style="font-size: smaller;"><a href="/wiki/%EC%98%81%EC%96%B4" title="영어">영어</a>: </span><span lang="en">Eisenstein integer</span>)는 아래의 꼴로 표현될 수 있는 <a href="/wiki/%EB%B3%B5%EC%86%8C%EC%88%98" title="복소수">복소수</a>를 말한다. <a href="/wiki/%EB%8F%85%EC%9D%BC" title="독일">독일</a>의 <a href="/wiki/%EC%88%98%ED%95%99%EC%9E%90" title="수학자">수학자</a> <a href="/wiki/%EA%B3%A0%ED%8A%B8%ED%99%80%ED%8A%B8_%EC%95%84%EC%9D%B4%EC%A0%A0%EC%8A%88%ED%83%80%EC%9D%B8" title="고트홀트 아이젠슈타인">고트홀트 아이젠슈타인</a>의 이름이 붙어 있다. </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 z=a+b\omega \qquad (a,b\in \mathbb {Z} )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>z</mi> <mo>=</mo> <mi>a</mi> <mo>+</mo> <mi>b</mi> <mi>ω</mi> <mspace width="2em" /> <mo stretchy="false">(</mo> <mi>a</mi> <mo>,</mo> <mi>b</mi> <mo>∈</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle z=a+b\omega \qquad (a,b\in \mathbb {Z} )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d23ebbab10bb68dbfcce792042483afbe4afe56a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:24.807ex; height:2.843ex;" alt="{\displaystyle z=a+b\omega \qquad (a,b\in \mathbb {Z} )}"></span></dd></dl> <p>여기서 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \omega }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ω</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \omega }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/48eff443f9de7a985bb94ca3bde20813ea737be8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.446ex; height:1.676ex;" alt="{\displaystyle \omega }"></span>는 <a href="/wiki/1%EC%9D%98_%EA%B1%B0%EB%93%AD%EC%A0%9C%EA%B3%B1%EA%B7%BC" title="1의 거듭제곱근">1의 세제곱근</a>이다. </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 \omega ={\frac {1}{2}}(-1+i{\sqrt {3}})=e^{2\pi i/3}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ω</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mo stretchy="false">(</mo> <mo>−</mo> <mn>1</mn> <mo>+</mo> <mi>i</mi> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>3</mn> </msqrt> </mrow> <mo stretchy="false">)</mo> <mo>=</mo> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> <mi>π</mi> <mi>i</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>3</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \omega ={\frac {1}{2}}(-1+i{\sqrt {3}})=e^{2\pi i/3}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec0963b96230b2bcaaf3b9206c40143d38eacbd1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:26.453ex; height:5.176ex;" alt="{\displaystyle \omega ={\frac {1}{2}}(-1+i{\sqrt {3}})=e^{2\pi i/3}}"></span></dd></dl> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="성질"><span id=".EC.84.B1.EC.A7.88"></span>성질</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%EC%95%84%EC%9D%B4%EC%A0%A0%EC%8A%88%ED%83%80%EC%9D%B8_%EC%A0%95%EC%88%98&action=edit&section=1" title="부분 편집: 성질"><span>편집</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>아이젠슈타인 정수는 <a href="/wiki/%EC%9B%90%EB%B6%84%EC%B2%B4" title="원분체">원분체</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathbb {Q} [\omega ]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Q</mi> </mrow> <mo stretchy="false">[</mo> <mi>ω</mi> <mo stretchy="false">]</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {Q} [\omega ]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ceabae545eae290d41ba8b5e717c6f8c45b241b0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.548ex; height:2.843ex;" alt="{\displaystyle \mathbb {Q} [\omega ]}"></span>의 <a href="/wiki/%EB%8C%80%EC%88%98%EC%A0%81_%EC%A0%95%EC%88%98%ED%99%98" class="mw-redirect" title="대수적 정수환">대수적 정수환</a>이며, <a href="/wiki/%EC%9C%A0%ED%81%B4%EB%A6%AC%EB%93%9C_%EC%A0%95%EC%97%AD" title="유클리드 정역">유클리드 정역</a>을 이룬다. 그 <a href="/wiki/%EA%B0%80%EC%97%AD%EC%9B%90%EA%B5%B0" class="mw-redirect" title="가역원군">가역원군</a>은 6개의 원소를 가지는 <a href="/wiki/%EC%88%9C%ED%99%98%EA%B5%B0" title="순환군">순환군</a>이며, 다음과 같다. </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 \{\pm 1,\pm \omega ,\pm \omega ^{2}\}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo fence="false" stretchy="false">{</mo> <mo>±</mo> <mn>1</mn> <mo>,</mo> <mo>±</mo> <mi>ω</mi> <mo>,</mo> <mo>±</mo> <msup> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo fence="false" stretchy="false">}</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \{\pm 1,\pm \omega ,\pm \omega ^{2}\}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/81a1ef06e920938bfbd2a8a7dd5be26f0ce3669c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:14.926ex; height:3.176ex;" alt="{\displaystyle \{\pm 1,\pm \omega ,\pm \omega ^{2}\}}"></span></dd></dl> <div class="mw-heading mw-heading2"><h2 id="아이젠슈타인_소수"><span id=".EC.95.84.EC.9D.B4.EC.A0.A0.EC.8A.88.ED.83.80.EC.9D.B8_.EC.86.8C.EC.88.98"></span>아이젠슈타인 소수</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%EC%95%84%EC%9D%B4%EC%A0%A0%EC%8A%88%ED%83%80%EC%9D%B8_%EC%A0%95%EC%88%98&action=edit&section=2" title="부분 편집: 아이젠슈타인 소수"><span>편집</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/%ED%8C%8C%EC%9D%BC:EisensteinPrimes-01.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/17/EisensteinPrimes-01.svg/220px-EisensteinPrimes-01.svg.png" decoding="async" width="220" height="191" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/17/EisensteinPrimes-01.svg/330px-EisensteinPrimes-01.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/17/EisensteinPrimes-01.svg/440px-EisensteinPrimes-01.svg.png 2x" data-file-width="360" data-file-height="313" /></a><figcaption>아이젠슈타인 소수</figcaption></figure> <p>아이젠슈타인 정수들은 <a href="/wiki/%EC%9C%A0%ED%81%B4%EB%A6%AC%EB%93%9C_%EC%A0%95%EC%97%AD" title="유클리드 정역">유클리드 정역</a>이므로, 유일 소인수분해를 가진다. 이에 따른 소수들을 <b>아이젠슈타인 소수</b>(<span style="font-size: smaller;"><a href="/wiki/%EC%98%81%EC%96%B4" title="영어">영어</a>: </span><span lang="en">Eisenstein prime</span>)라고 한다. 이들은 다음과 같다. (편의상, 통상적인, 즉 <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>에서의 소수를 유리소수라고 하자.) </p><p>아이젠슈타인 정수 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle z=a+b\omega }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>z</mi> <mo>=</mo> <mi>a</mi> <mo>+</mo> <mi>b</mi> <mi>ω</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle z=a+b\omega }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/831a7cd52fccc8fc17822deddfec0a21a46afea9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:10.7ex; height:2.343ex;" alt="{\displaystyle z=a+b\omega }"></span>가 아이젠슈타인 소수일 필요충분조건은 다음과 같다. </p> <ol><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle z}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>z</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle z}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bf368e72c009decd9b6686ee84a375632e11de98" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.088ex; height:1.676ex;" alt="{\displaystyle z}"></span>는 <a href="/wiki/%EA%B0%80%EC%97%AD%EC%9B%90" title="가역원">가역원</a>과 <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 p\equiv 2{\pmod {3}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> <mo>≡</mo> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mspace width="1em" /> <mo stretchy="false">(</mo> <mi>mod</mi> <mspace width="0.333em" /> <mn>3</mn> <mo stretchy="false">)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p\equiv 2{\pmod {3}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/292b998f52f62122748660670874177bc85065f8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; margin-left: -0.089ex; width:16.366ex; height:2.843ex;" alt="{\displaystyle p\equiv 2{\pmod {3}}}"></span>인 유리소수 <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 p}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/81eac1e205430d1f40810df36a0edffdc367af36" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:1.259ex; height:2.009ex;" alt="{\displaystyle p}"></span>의 곱과 같거나,</li> <li>아니면 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle |z|^{2}=a^{2}-ab+b^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>z</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mi>a</mi> <mi>b</mi> <mo>+</mo> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle |z|^{2}=a^{2}-ab+b^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/621d7082e054b5956f79b8705faad4719d9128df" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:18.779ex; height:3.343ex;" alt="{\displaystyle |z|^{2}=a^{2}-ab+b^{2}}"></span>는 유리소수이다. (이 경우 항상 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle |z|^{2}\equiv 0,1{\pmod {3}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mi>z</mi> <msup> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">|</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>≡</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mspace width="1em" /> <mo stretchy="false">(</mo> <mi>mod</mi> <mspace width="0.333em" /> <mn>3</mn> <mo stretchy="false">)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle |z|^{2}\equiv 0,1{\pmod {3}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c45b78004b52802dfeb097ed098e15692a21ea44" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:20.74ex; height:3.343ex;" alt="{\displaystyle |z|^{2}\equiv 0,1{\pmod {3}}}"></span>이다.)</li></ol> <p>따라서, 아이젠슈타인 소수의 목록은 다음과 같다. </p> <ul><li>갈리지 않는 (유리소수인) 아이젠슈타인 소수.</li></ul> <dl><dd><dl><dd>2, 5, 11, 17, 23, 29, 41, 47, 53, 59, 71, 83, 89, 101, … (<a href="/wiki/%EC%98%A8%EB%9D%BC%EC%9D%B8_%EC%A0%95%EC%88%98%EC%97%B4_%EC%82%AC%EC%A0%84" title="온라인 정수열 사전">OEIS</a>의 수열 <a href="//oeis.org/A3627" class="extiw" title="oeis:A3627">A3627</a>)</dd></dl></dd></dl> <ul><li>실수가 아닌 아이젠슈타인 소수</li></ul> <dl><dd><dl><dd>2 + ω, 3 + ω, 4 + ω, 5 + 2ω, 6 + ω, 7 + ω, 7 + 3ω, …</dd></dl></dd></dl> <p>유리소수이지만 아이젠슈타인 소수가 아닌 수들은 다음과 같다. </p> <dl><dd>3 = −(1 + 2ω)<sup>2</sup>, 7 = (3 + ω)(2 − ω), … (<a href="/wiki/%EC%98%A8%EB%9D%BC%EC%9D%B8_%EC%A0%95%EC%88%98%EC%97%B4_%EC%82%AC%EC%A0%84" title="온라인 정수열 사전">OEIS</a>의 수열 <a href="//oeis.org/A7645" class="extiw" title="oeis:A7645">A7645</a>)</dd></dl> <div class="mw-heading mw-heading2"><h2 id="외부_링크"><span id=".EC.99.B8.EB.B6.80_.EB.A7.81.ED.81.AC"></span>외부 링크</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%EC%95%84%EC%9D%B4%EC%A0%A0%EC%8A%88%ED%83%80%EC%9D%B8_%EC%A0%95%EC%88%98&action=edit&section=3" title="부분 편집: 외부 링크"><span>편집</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><cite class="citation web">Weisstein, Eric Wolfgang. <a rel="nofollow" class="external text" href="https://mathworld.wolfram.com/EisensteinInteger.html">“Eisenstein integer”</a>. 《<a href="/wiki/%EB%A7%A4%EC%8A%A4%EC%9B%94%EB%93%9C" title="매스월드">Wolfram MathWorld</a>》 (영어). Wolfram Research.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Wolfram+MathWorld&rft.atitle=Eisenstein+integer&rft.aulast=Weisstein&rft.aufirst=Eric+Wolfgang&rft_id=https%3A%2F%2Fmathworld.wolfram.com%2FEisensteinInteger.html&rfr_id=info%3Asid%2Fko.wikipedia.org%3A%EC%95%84%EC%9D%B4%EC%A0%A0%EC%8A%88%ED%83%80%EC%9D%B8+%EC%A0%95%EC%88%98" class="Z3988"><span style="display:none;"> </span></span></li> <li><cite class="citation web">Weisstein, Eric Wolfgang. <a rel="nofollow" class="external text" href="https://mathworld.wolfram.com/EisensteinPrime.html">“Eisenstein prime”</a>. 《<a href="/wiki/%EB%A7%A4%EC%8A%A4%EC%9B%94%EB%93%9C" title="매스월드">Wolfram MathWorld</a>》 (영어). Wolfram Research.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=unknown&rft.jtitle=Wolfram+MathWorld&rft.atitle=Eisenstein+prime&rft.aulast=Weisstein&rft.aufirst=Eric+Wolfgang&rft_id=https%3A%2F%2Fmathworld.wolfram.com%2FEisensteinPrime.html&rfr_id=info%3Asid%2Fko.wikipedia.org%3A%EC%95%84%EC%9D%B4%EC%A0%A0%EC%8A%88%ED%83%80%EC%9D%B8+%EC%A0%95%EC%88%98" class="Z3988"><span style="display:none;"> </span></span></li></ul> <div class="mw-heading mw-heading2"><h2 id="같이_보기"><span id=".EA.B0.99.EC.9D.B4_.EB.B3.B4.EA.B8.B0"></span>같이 보기</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%EC%95%84%EC%9D%B4%EC%A0%A0%EC%8A%88%ED%83%80%EC%9D%B8_%EC%A0%95%EC%88%98&action=edit&section=4" title="부분 편집: 같이 보기"><span>편집</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/%EA%B0%80%EC%9A%B0%EC%8A%A4_%EC%A0%95%EC%88%98" title="가우스 정수">가우스 정수</a></li> <li><a href="/wiki/%EC%9D%B4%EC%B0%A8_%EC%A0%95%EC%88%98" class="mw-redirect" title="이차 정수">이차 정수</a></li></ul> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r36480591">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul ol,.mw-parser-output .hlist ul ul{display:inline}.mw-parser-output .hlist .mw-empty-li{display:none}.mw-parser-output .hlist dt::after{content:": "}.mw-parser-output .hlist dd::after,.mw-parser-output .hlist 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tr+tr>.navbox-abovebelow,.mw-parser-output tr+tr>.navbox-group,.mw-parser-output tr+tr>.navbox-image,.mw-parser-output tr+tr>.navbox-list{border-top:2px solid #fdfdfd}.mw-parser-output .navbox-title{background-color:#ccf}.mw-parser-output .navbox-abovebelow,.mw-parser-output .navbox-group,.mw-parser-output .navbox-subgroup .navbox-title{background-color:#ddf}.mw-parser-output .navbox-subgroup .navbox-group,.mw-parser-output .navbox-subgroup .navbox-abovebelow{background-color:#e6e6ff}.mw-parser-output .navbox-even{background-color:#f7f7f7}.mw-parser-output .navbox-odd{background-color:transparent}.mw-parser-output .navbox .hlist td dl,.mw-parser-output .navbox .hlist td ol,.mw-parser-output .navbox .hlist td ul,.mw-parser-output .navbox td.hlist dl,.mw-parser-output .navbox td.hlist ol,.mw-parser-output .navbox td.hlist ul{padding:0.125em 0}.mw-parser-output .navbox .navbar{display:block;font-size:100%}.mw-parser-output .navbox-title .navbar{float:left;text-align:left;margin-right:0.5em}</style></div><div role="navigation" class="navbox" aria-labelledby="수_체계" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r36480591"><style data-mw-deduplicate="TemplateStyles:r34311309">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-보기"><a href="/wiki/%ED%8B%80:%EC%88%98_%EC%B2%B4%EA%B3%84" title="틀:수 체계"><abbr title="이 틀을 보기" style=";;background:none transparent;border:none;box-shadow:none;padding:0;">v</abbr></a></li><li class="nv-토론"><a href="/wiki/%ED%8B%80%ED%86%A0%EB%A1%A0:%EC%88%98_%EC%B2%B4%EA%B3%84" title="틀토론:수 체계"><abbr title="이 틀에 관해 토론하기" style=";;background:none transparent;border:none;box-shadow:none;padding:0;">t</abbr></a></li><li class="nv-편집"><a href="/wiki/%ED%8A%B9%EC%88%98:%EB%AC%B8%EC%84%9C%ED%8E%B8%EC%A7%91/%ED%8B%80:%EC%88%98_%EC%B2%B4%EA%B3%84" title="특수:문서편집/틀:수 체계"><abbr title="이 틀을 편집하기" style=";;background:none transparent;border:none;box-shadow:none;padding:0;">e</abbr></a></li></ul></div><div id="수_체계" style="font-size:114%;margin:0 4em"><a href="/wiki/%EC%88%98_(%EC%88%98%ED%95%99)" title="수 (수학)">수</a> 체계</div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">복소수</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/%EC%9E%90%EC%97%B0%EC%88%98" title="자연수">자연수</a> (ℕ)</li> <li><a href="/wiki/%EC%A0%95%EC%88%98" title="정수">정수</a> (ℤ)</li> <li><a href="/wiki/%EC%9C%A0%EB%A6%AC%EC%88%98" title="유리수">유리수</a> (ℚ)</li> <li><a href="/wiki/%EB%AC%B4%EB%A6%AC%EC%88%98" title="무리수">무리수</a> (ℝ∖ℚ)</li> <li><a href="/wiki/%EC%8B%A4%EC%88%98" title="실수">실수</a> (ℝ)</li> <li><a href="/wiki/%ED%97%88%EC%88%98" title="허수">허수</a> (ℂ∖ℝ)</li> <li><a href="/wiki/%EB%B3%B5%EC%86%8C%EC%88%98" title="복소수">복소수</a> (ℂ)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">자연수의 분류</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/%EC%86%8C%EC%88%98_(%EC%88%98%EB%A1%A0)" title="소수 (수론)">소수</a> (ℙ)</li> <li><a href="/wiki/%ED%95%A9%EC%84%B1%EC%88%98" title="합성수">합성수</a> (ℕ∖ℙ∖{0,1})</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">유리수의 분류</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/%EB%B0%98%EC%A0%95%EC%88%98" title="반정수">반정수</a> (1/2+ℤ)</li> <li><a href="/wiki/%EC%9D%B4%EC%A7%84_%EC%9C%A0%EB%A6%AC%EC%88%98" title="이진 유리수">이진 유리수</a> ((2<sup>ℕ</sup>)<sup>-1</sup>ℤ)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">실수의 분류</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/%EC%96%91%EC%88%98_(%EC%88%98%ED%95%99)" title="양수 (수학)">양수</a> (ℝ<sup>+</sup>)</li> <li><a href="/wiki/%EC%9D%8C%EC%88%98" title="음수">음수</a> (ℝ<sup>-</sup>)</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">복소수의 분류</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/%EB%8C%80%EC%88%98%EC%A0%81_%EC%88%98" title="대수적 수">대수적 수</a> (<span class="sfrac nowrap;"><span style="display:none; display:inline-block; text-align:center;"><span style="display:block; line-height:0.4em; font-size:70%; padding:0 0.1em;">—</span><span style="display:block; line-height:1em; padding:0 0.1em;">ℚ</span></span></span>)</li> <li><a href="/wiki/%EC%B4%88%EC%9B%94%EC%88%98" title="초월수">초월수</a> (ℂ∖<span class="sfrac nowrap;"><span style="display:none; display:inline-block; text-align:center;"><span style="display:block; line-height:0.4em; font-size:70%; padding:0 0.1em;">—</span><span style="display:block; line-height:1em; padding:0 0.1em;">ℚ</span></span></span>)</li> <li><a href="/wiki/%EB%8C%80%EC%88%98%EC%A0%81_%EC%A0%95%EC%88%98" class="mw-redirect" title="대수적 정수">대수적 정수</a> (<span class="mathcal" style="font-family: 'Lucida Calligraphy', 'Monotype Corsiva', 'URW Chancery L', 'Apple Chancery', serif;">O</span><sub><span class="sfrac nowrap;"><span style="display:none; display:inline-block; text-align:center;"><span style="display:block; line-height:0.4em; font-size:70%; padding:0 0.1em;">—</span><span style="display:block; line-height:1em; padding:0 0.1em;">ℚ</span></span></span></sub>)</li> <li><a href="/wiki/%EA%B0%80%EC%9A%B0%EC%8A%A4_%EC%A0%95%EC%88%98" title="가우스 정수">가우스 정수</a> (ℤ[i])</li> <li><a class="mw-selflink selflink">아이젠슈타인 정수</a> (<span class="mathcal" style="font-family: 'Lucida Calligraphy', 'Monotype Corsiva', 'URW Chancery L', 'Apple Chancery', serif;">O</span><sub>ℚ(√-3)</sub>)</li> <li><a href="/wiki/%EC%9E%91%EB%8F%84_%EA%B0%80%EB%8A%A5%ED%95%9C_%EC%88%98" title="작도 가능한 수">작도 가능한 수</a></li> <li><a href="/wiki/%EA%B3%84%EC%82%B0_%EA%B0%80%EB%8A%A5%ED%95%9C_%EC%88%98" title="계산 가능한 수">계산 가능한 수</a></li> <li><a href="/wiki/%EC%A0%95%EC%9D%98_%EA%B0%80%EB%8A%A5%ED%95%9C_%EC%88%98" title="정의 가능한 수">정의 가능한 수</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">기타</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><a href="/wiki/%EC%9D%B4%EC%9B%90%EC%88%98_(%EC%88%98%ED%95%99)" title="이원수 (수학)">이원수</a> (ℝ[x]/(x<sup>2</sup>))</li> <li><a href="/w/index.php?title=%EB%8B%A4%EC%9B%90%EC%88%98&action=edit&redlink=1" class="new" title="다원수 (없는 문서)">다원수</a></li> <li><a href="/wiki/%EC%82%AC%EC%9B%90%EC%88%98" title="사원수">사원수</a> (ℍ)</li> <li><a href="/wiki/%ED%8C%94%EC%9B%90%EC%88%98" title="팔원수">팔원수</a> (𝕆)</li> <li><a href="/wiki/%EC%8B%AD%EC%9C%A1%EC%9B%90%EC%88%98" title="십육원수">십육원수</a> (𝕊)</li> <li><a href="/wiki/P%EC%A7%84%EC%88%98" title="P진수">p진수</a> (ℚ<sub>p</sub>)</li> <li><a href="/wiki/%EC%B4%88%EC%8B%A4%EC%88%98" title="초실수">초실수</a></li> <li><a href="/w/index.php?title=%EC%83%81%EC%B4%88%EC%8B%A4%EC%88%98&action=edit&redlink=1" class="new" title="상초실수 (없는 문서)">상초실수</a></li> <li><a href="/wiki/%EC%B4%88%ED%98%84%EC%8B%A4%EC%88%98" title="초현실수">초현실수</a></li> <li><a href="/wiki/%EC%88%9C%EC%84%9C%EC%88%98" title="순서수">순서수</a> (Ord)</li> <li><a href="/wiki/%EA%B8%B0%EC%88%98_(%EC%88%98%ED%95%99)" title="기수 (수학)">기수</a> (Card)</li></ul> </div></td></tr></tbody></table></div> <table class="notice metadata plainlinks stub" style="clear: both; font-size: smaller;"> <tbody><tr> <td style="width: 40px;"><span typeof="mw:File"><a href="/wiki/%EB%B6%84%EB%A5%98:%EC%88%98%ED%95%99%EC%97%90_%EA%B4%80%ED%95%9C_%ED%86%A0%EB%A7%89%EA%B8%80" title="분류:수학에 관한 토막글"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1e/Circle-icons-calculator.svg/40px-Circle-icons-calculator.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1e/Circle-icons-calculator.svg/60px-Circle-icons-calculator.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1e/Circle-icons-calculator.svg/80px-Circle-icons-calculator.svg.png 2x" data-file-width="512" data-file-height="512" /></a></span> </td> <td>이 글은 수학에 관한 <a href="/wiki/%EC%9C%84%ED%82%A4%EB%B0%B1%EA%B3%BC:%ED%86%A0%EB%A7%89%EA%B8%80" title="위키백과:토막글">토막글</a>입니다. 여러분의 지식으로 알차게 <a class="external text" href="https://ko.wikipedia.org/w/index.php?title=%EC%95%84%EC%9D%B4%EC%A0%A0%EC%8A%88%ED%83%80%EC%9D%B8_%EC%A0%95%EC%88%98&action=edit">문서를 완성해</a> 갑시다. </td></tr> </tbody></table>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">원본 주소 "<a dir="ltr" href="https://ko.wikipedia.org/w/index.php?title=아이젠슈타인_정수&oldid=35543358">https://ko.wikipedia.org/w/index.php?title=아이젠슈타인_정수&oldid=35543358</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/%ED%8A%B9%EC%88%98:%EB%B6%84%EB%A5%98" title="특수:분류">분류</a>: <ul><li><a href="/wiki/%EB%B6%84%EB%A5%98:%EB%B3%B5%EC%86%8C%EC%88%98" title="분류:복소수">복소수</a></li><li><a href="/wiki/%EB%B6%84%EB%A5%98:%EA%B2%A9%EC%9E%90%EC%A0%90" title="분류:격자점">격자점</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">숨은 분류: <ul><li><a href="/wiki/%EB%B6%84%EB%A5%98:%ED%95%B4%EA%B2%B0%EB%90%98%EC%A7%80_%EC%95%8A%EC%9D%80_%EC%86%8D%EC%84%B1%EC%9D%B4_%EC%9E%88%EB%8A%94_%EB%AC%B8%EC%84%9C" title="분류:해결되지 않은 속성이 있는 문서">해결되지 않은 속성이 있는 문서</a></li><li><a href="/wiki/%EB%B6%84%EB%A5%98:%EC%9C%84%ED%82%A4%EB%8D%B0%EC%9D%B4%ED%84%B0_%EC%86%8D%EC%84%B1_P373%EC%9D%84_%EC%82%AC%EC%9A%A9%ED%95%98%EB%8A%94_%EB%AC%B8%EC%84%9C" title="분류:위키데이터 속성 P373을 사용하는 문서">위키데이터 속성 P373을 사용하는 문서</a></li><li><a href="/wiki/%EB%B6%84%EB%A5%98:%EC%9C%84%ED%82%A4%EB%8D%B0%EC%9D%B4%ED%84%B0_%EC%86%8D%EC%84%B1_P7859%EB%A5%BC_%EC%82%AC%EC%9A%A9%ED%95%98%EB%8A%94_%EB%AC%B8%EC%84%9C" title="분류:위키데이터 속성 P7859를 사용하는 문서">위키데이터 속성 P7859를 사용하는 문서</a></li><li><a href="/wiki/%EB%B6%84%EB%A5%98:%EC%98%81%EC%96%B4_%ED%91%9C%EA%B8%B0%EB%A5%BC_%ED%8F%AC%ED%95%A8%ED%95%9C_%EB%AC%B8%EC%84%9C" title="분류:영어 표기를 포함한 문서">영어 표기를 포함한 문서</a></li><li><a href="/wiki/%EB%B6%84%EB%A5%98:CS1_-_%EC%98%81%EC%96%B4_%EC%9D%B8%EC%9A%A9_(en)" title="분류:CS1 - 영어 인용 (en)">CS1 - 영어 인용 (en)</a></li><li><a href="/wiki/%EB%B6%84%EB%A5%98:%EC%88%98%ED%95%99%EC%97%90_%EA%B4%80%ED%95%9C_%ED%86%A0%EB%A7%89%EA%B8%80" title="분류:수학에 관한 토막글">수학에 관한 토막글</a></li><li><a href="/wiki/%EB%B6%84%EB%A5%98:%EB%AA%A8%EB%93%A0_%ED%86%A0%EB%A7%89%EA%B8%80_%EB%AC%B8%EC%84%9C" title="분류:모든 토막글 문서">모든 토막글 문서</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> 이 문서는 2023년 9월 8일 (금) 23:38에 마지막으로 편집되었습니다.</li> <li id="footer-info-copyright">모든 문서는 <a rel="nofollow" class="external text" href="//creativecommons.org/licenses/by-sa/4.0/deed.ko">크리에이티브 커먼즈 저작자표시-동일조건변경허락 4.0</a>에 따라 사용할 수 있으며, 추가적인 조건이 적용될 수 있습니다. 자세한 내용은 <a class="external text" href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Terms_of_Use/ko">이용 약관</a>을 참고하십시오.<br />Wikipedia®는 미국 및 다른 국가에 등록되어 있는 <a rel="nofollow" class="external text" href="https://www.wikimediafoundation.org">Wikimedia Foundation, Inc.</a> 소유의 등록 상표입니다.</li> </ul> <ul id="footer-places"> <li id="footer-places-privacy"><a 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