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작은숲:공책/가환대수/Zariski continous function between two rings - 편집 역사
2026-08-19T21:52:09Z
이 문서의 편집 역사
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Utolee90: 개인적으로 작성된 내용이므로 퍼옴틀 삭제
2017-04-08T10:04:53Z
<p>개인적으로 작성된 내용이므로 퍼옴틀 삭제</p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">2017년 4월 8일 (토) 19:04 판</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{공책}}</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{공책}}</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">{{퍼옴|[https://studynotekr.miraheze.org/wiki/Study_Note:Math-CA/Zariski_continous_function_between_two_rings Korean Study Note]}}</del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{작성중}}</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>{{작성중}}</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>This is about the explanation of Zariski continuity of Algebraic function <math>f:R \to S </math></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>This is about the explanation of Zariski continuity of Algebraic function <math>f:R \to S </math></div></td></tr>
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Utolee90: removed Category:큰숲백과 공책; added Category:큰숲공책 using HotCat
2017-02-19T14:56:47Z
<p>removed <a href="/w/index.php?title=%EB%B6%84%EB%A5%98:%ED%81%B0%EC%88%B2%EB%B0%B1%EA%B3%BC_%EA%B3%B5%EC%B1%85&action=edit&redlink=1" class="new" title="분류:큰숲백과 공책 (없는 문서)">Category:큰숲백과 공책</a>; added <a href="/wiki/%EB%B6%84%EB%A5%98:%ED%81%B0%EC%88%B2%EA%B3%B5%EC%B1%85" title="분류:큰숲공책">Category:큰숲공책</a> using <a href="/w/index.php?title=%EB%8F%84%EC%9B%80%EB%A7%90:Gadget-HotCat&action=edit&redlink=1" class="new" title="도움말:Gadget-HotCat (없는 문서)">HotCat</a></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">2017년 2월 19일 (일) 23:56 판</td>
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Utolee90: /* 4 */ 오류 정정
2017-02-19T14:56:26Z
<p><span class="autocomment">4: </span> 오류 정정</p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">2017년 2월 19일 (일) 23:56 판</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l24">24번째 줄:</td>
<td colspan="2" class="diff-lineno">24번째 줄:</td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>=== 4 ===</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>=== 4 ===</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>: ''' iv) ''' If <math> \phi</math> is surjective, then <math>\phi*</math> is a homeomorphism of Y onto the closed subset <math>V(Ker (\phi))</math> of ''X''. In particular, Spec(''A'') and <math>\rm{Spec} (\it{A/ \Re})</math></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>: ''' iv) ''' If <math> \phi</math> is surjective, then <math>\phi*</math> is a homeomorphism of Y onto the closed subset <math>V(Ker (\phi))</math> of ''X''. In particular, Spec(''A'') and <math>\rm{Spec} (\it{A/ \Re})</math></div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>{{접기|Solution| Suppose <math>\phi</math> is surjective, then by lattice isomorphism theorem, there is a bijective relation between ideal ''p'' of ''A'' containing <math>\ker \phi</math> and the ideal <math>\phi(p)</math> of <math>B=A/\ker(\phi)</math>. Especially, take <math>q {\triangleleft}_{\rm{pr}} \it B</math>. Then <math>\phi*(q) {\vartriangleleft}_{\rm{pr}} \it A</math> satisfies <math>\phi(q)^{\ast}/\ker(\phi) \cong q </math>. Also, <math>\phi^{\ast}</math> is a homeomorphism because for any ideal <math> I \triangleleft B </math>, <math>{\phi}^{\ast}(I)</math> is also an ideal and there is a one-two-one correspondence between <math>V(\p)</math> and <math>V(\phi^{-1} (\p )</math> for any <math>p \supset I </math>. That is, <math>\phi^{\ast}</math> sends V(I) to <math>V(\phi^{-1} (I))</math>. Thus, <math>\phi^{\ast}</math> is a homeomorphism between <math>\rm{Spec} (\it{B})</math> and <math> V(\ker (\phi))</math>.}}</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>{{접기|Solution| Suppose <math>\phi</math> is surjective, then by lattice isomorphism theorem, there is a bijective relation between ideal ''p'' of ''A'' containing <math>\ker \phi</math> and the ideal <math>\phi(p)</math> of <math>B=A/\ker(\phi)</math>. Especially, take <math>q {\triangleleft}_{\rm{pr}} \it B</math>. Then <math>\phi*(q) {\vartriangleleft}_{\rm{pr}} \it A</math> satisfies <math>\phi(q)^{\ast}/\ker(\phi) \cong q </math>. Also, <math>\phi^{\ast}</math> is a homeomorphism because for any ideal <math> I \triangleleft B </math>, <math>{\phi}^{\ast}(I)</math> is also an ideal and there is a one-two-one correspondence between <math>V(\<ins style="font-weight: bold; text-decoration: none;">text{</ins>p<ins style="font-weight: bold; text-decoration: none;">}</ins>)</math> and <math>V(\phi^{-1} (\<ins style="font-weight: bold; text-decoration: none;">text{</ins>p<ins style="font-weight: bold; text-decoration: none;">} </ins>)</math> for any <math>p \supset I </math>. That is, <math>\phi^{\ast}</math> sends V(I) to <math>V(\phi^{-1} (I))</math>. Thus, <math>\phi^{\ast}</math> is a homeomorphism between <math>\rm{Spec} (\it{B})</math> and <math> V(\ker (\phi))</math>.}}</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>=== 5 ===</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>=== 5 ===</div></td></tr>
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Utolee90: /* 3 */
2017-02-18T23:01:33Z
<p><span class="autocomment">3</span></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">2017년 2월 19일 (일) 08:01 판</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l19">19번째 줄:</td>
<td colspan="2" class="diff-lineno">19번째 줄:</td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>=== 3 ===</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>=== 3 ===</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>: ''' iii)''' If <math>b</math> is an ideal of B, then <math>\bar{\phi^{\ast}(V(b))} =V( b^c )</math>.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>: ''' iii)''' If <math>b</math> is an ideal of B, then <math>\bar{\phi^{\ast}(V(b))} =V( b^c )</math>.</div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>{{<del style="font-weight: bold; text-decoration: none;">숨기기</del>|Solution| Let <math>p \triangleleft_pr A</math> Then <math> p \in \phi^{\ast} (V(b)) \Leftrightarrow p \supset \phi^{-1}(b) \Leftrightarrow p \in V( b^c ) </math> and <math> \phi^{\ast} (V(b)) = V( b^c ) </math> <br></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>{{<ins style="font-weight: bold; text-decoration: none;">접기</ins>|Solution| Let <math>p \triangleleft_pr A</math> Then <math> p \in \phi^{\ast} (V(b)) \Leftrightarrow p \supset \phi^{-1}(b) \Leftrightarrow p \in V( b^c ) </math> and <math> \phi^{\ast} (V(b)) = V( b^c ) </math> <br></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Meanwhile, <math>p \in V(b^c ) \Leftrightarrow p \supset \phi^{-1} (b).</math> and take a set <math>\bar{\phi^{/ast} (V(b))} {{=}} V(\phi^{ast}(b))</math> and <math>p \in V(\phi^{\ast}(b)) =V(b^c )</math>. So <math>\bar{\phi^{\ast} (V(b))} {{=}} V(b^c ).</math> is a prime ideal of ''A'' satisfying <math>\phi^/\ker (\phi)=q </math> }}</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Meanwhile, <math>p \in V(b^c ) \Leftrightarrow p \supset \phi^{-1} (b).</math> and take a set <math>\bar{\phi^{/ast} (V(b))} {{=}} V(\phi^{ast}(b))</math> and <math>p \in V(\phi^{\ast}(b)) =V(b^c )</math>. So <math>\bar{\phi^{\ast} (V(b))} {{=}} V(b^c ).</math> is a prime ideal of ''A'' satisfying <math>\phi^/\ker (\phi)=q </math> }}</div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;"></ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>=== 4 ===</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>=== 4 ===</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>: ''' iv) ''' If <math> \phi</math> is surjective, then <math>\phi*</math> is a homeomorphism of Y onto the closed subset <math>V(Ker (\phi))</math> of ''X''. In particular, Spec(''A'') and <math>\rm{Spec} (\it{A/ \Re})</math></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>: ''' iv) ''' If <math> \phi</math> is surjective, then <math>\phi*</math> is a homeomorphism of Y onto the closed subset <math>V(Ker (\phi))</math> of ''X''. In particular, Spec(''A'') and <math>\rm{Spec} (\it{A/ \Re})</math></div></td></tr>
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Utolee90: /* 4 */
2017-02-18T23:00:57Z
<p><span class="autocomment">4</span></p>
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</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l23">23번째 줄:</td>
<td colspan="2" class="diff-lineno">23번째 줄:</td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>=== 4 ===</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>=== 4 ===</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>: ''' iv) ''' If <math> \phi</math> is surjective, then <math>\phi*</math> is a homeomorphism of Y onto the closed subset <math>V(Ker (\phi))</math> of ''X''. In particular, Spec(''A'') and <math>\rm{Spec} (\it{A/ \Re})</math></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>: ''' iv) ''' If <math> \phi</math> is surjective, then <math>\phi*</math> is a homeomorphism of Y onto the closed subset <math>V(Ker (\phi))</math> of ''X''. In particular, Spec(''A'') and <math>\rm{Spec} (\it{A/ \Re})</math></div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>{{<del style="font-weight: bold; text-decoration: none;">숨기기</del>|Solution| Suppose <math>\phi</math> is surjective, then by lattice isomorphism theorem, there is a bijective relation between ideal ''p'' of ''A'' containing <math>\ker \phi</math> and the ideal <math>\phi(p)</math> of <math>B=A/\ker(\phi)</math>. Especially, take <math>q {\triangleleft}_{\rm{pr}} \it B</math>. Then <math>\phi*(q) {\vartriangleleft}_{\rm{pr}} \it A</math> satisfies <math>\phi(q)^{\ast}/\ker(\phi) \cong q </math>. Also, <math>\phi^{\ast}</math> is a homeomorphism because for any ideal <math> I \triangleleft B </math>, <math>{\phi}^{\ast}(I)</math> is also an ideal and there is a one-two-one correspondence between <math>V(\p)</math> and <math>V(\phi^{-1} (\p )</math> for any <math>p \supset I </math>. That is, <math>\phi^{\ast}</math> sends V(I) to <math>V(\phi^{-1} (I))</math>. Thus, <math>\phi^{\ast}</math> is a homeomorphism between <math>\rm{Spec} (\it{B})</math> and <math> V(\ker (\phi))</math>.}}</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>{{<ins style="font-weight: bold; text-decoration: none;">접기</ins>|Solution| Suppose <math>\phi</math> is surjective, then by lattice isomorphism theorem, there is a bijective relation between ideal ''p'' of ''A'' containing <math>\ker \phi</math> and the ideal <math>\phi(p)</math> of <math>B=A/\ker(\phi)</math>. Especially, take <math>q {\triangleleft}_{\rm{pr}} \it B</math>. Then <math>\phi*(q) {\vartriangleleft}_{\rm{pr}} \it A</math> satisfies <math>\phi(q)^{\ast}/\ker(\phi) \cong q </math>. Also, <math>\phi^{\ast}</math> is a homeomorphism because for any ideal <math> I \triangleleft B </math>, <math>{\phi}^{\ast}(I)</math> is also an ideal and there is a one-two-one correspondence between <math>V(\p)</math> and <math>V(\phi^{-1} (\p )</math> for any <math>p \supset I </math>. That is, <math>\phi^{\ast}</math> sends V(I) to <math>V(\phi^{-1} (I))</math>. Thus, <math>\phi^{\ast}</math> is a homeomorphism between <math>\rm{Spec} (\it{B})</math> and <math> V(\ker (\phi))</math>.}}</div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>=== 5 ===</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>=== 5 ===</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>: ''' v) ''' If φ is injective, then <math>\phi^{\ast} (Y) </math> is dense in X. More precisely, <math>\phi^{\ast}(Y)</math> is dense in <math>X \Leftrightarrow \ker (\phi) \subseteq \rm{Nil}(\it{A})</math></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>: ''' v) ''' If φ is injective, then <math>\phi^{\ast} (Y) </math> is dense in X. More precisely, <math>\phi^{\ast}(Y)</math> is dense in <math>X \Leftrightarrow \ker (\phi) \subseteq \rm{Nil}(\it{A})</math></div></td></tr>
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Utolee90: /* 5 */
2017-02-18T23:00:30Z
<p><span class="autocomment">5</span></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">2017년 2월 19일 (일) 08:00 판</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l26">26번째 줄:</td>
<td colspan="2" class="diff-lineno">26번째 줄:</td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>=== 5 ===</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>=== 5 ===</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>: ''' v) ''' If φ is injective, then <math>\phi^{\ast} (Y) </math> is dense in X. More precisely, <math>\phi^{\ast}(Y)</math> is dense in <math>X \Leftrightarrow \ker (\phi) \subseteq \rm{Nil}(\it{A})</math></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>: ''' v) ''' If φ is injective, then <math>\phi^{\ast} (Y) </math> is dense in X. More precisely, <math>\phi^{\ast}(Y)</math> is dense in <math>X \Leftrightarrow \ker (\phi) \subseteq \rm{Nil}(\it{A})</math></div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>{{<del style="font-weight: bold; text-decoration: none;">숨기기</del>|Solution|</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>{{<ins style="font-weight: bold; text-decoration: none;">접기</ins>|Solution|</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Suppose <math>\phi^{\ast} (Y)</math> is dense, then the set </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Suppose <math>\phi^{\ast} (Y)</math> is dense, then the set </div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>}}</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>}}</div></td></tr>
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Utolee90: /* External Links */
2017-02-18T22:59:59Z
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== External Links ==</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>== External Links ==</div></td></tr>
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큰숲백과>Daelim: Daelim님이 큰숲백과:공책/가환대수/Zariski continous function between two rings 문서를 넘겨주기를 만들지 않고 Tinyforest:공책/가환대수/Zariski continous function between two rings 문서로 이동했습니다
2017-02-13T05:32:32Z
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큰숲백과>Daelim: Daelim님이 공책/가환대수/Zariski continous function between two rings 문서를 큰숲백과:공책/가환대수/Zariski continous function between two rings 문서로 이동했습니다
2017-02-13T05:32:15Z
<p>Daelim님이 <a href="/wiki/%EA%B3%B5%EC%B1%85/%EA%B0%80%ED%99%98%EB%8C%80%EC%88%98/Zariski_continous_function_between_two_rings" class="mw-redirect" title="공책/가환대수/Zariski continous function between two rings">공책/가환대수/Zariski continous function between two rings</a> 문서를 <a href="/w/index.php?title=%ED%81%B0%EC%88%B2%EB%B0%B1%EA%B3%BC:%EA%B3%B5%EC%B1%85/%EA%B0%80%ED%99%98%EB%8C%80%EC%88%98/Zariski_continous_function_between_two_rings&action=edit&redlink=1" class="new" title="큰숲백과:공책/가환대수/Zariski continous function between two rings (없는 문서)">큰숲백과:공책/가환대수/Zariski continous function between two rings</a> 문서로 이동했습니다</p>
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2017-02-09T13:38:50Z
<p>Utolee90님이 <a href="/wiki/%EA%B3%B5%EC%B1%85:%EA%B0%80%ED%99%98%EB%8C%80%EC%88%98/Zariski_continous_function_between_two_rings" class="mw-redirect" title="공책:가환대수/Zariski continous function between two rings">공책:가환대수/Zariski continous function between two rings</a> 문서를 <a href="/wiki/%EA%B3%B5%EC%B1%85/%EA%B0%80%ED%99%98%EB%8C%80%EC%88%98/Zariski_continous_function_between_two_rings" class="mw-redirect" title="공책/가환대수/Zariski continous function between two rings">공책/가환대수/Zariski continous function between two rings</a> 문서로 이동했습니다</p>
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