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<title>sun123zxy&#39;s blog</title>
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<description>Atiyah--Macdonald affairs.</description>
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<item>
  <title>DVR–Dedekind 乱炖</title>
  <dc:creator>sun123zxy </dc:creator>
  <link>https://blog.sun123zxy.top/posts/20260406-dvr-dedekind/</link>
  <description><![CDATA[ <a href="../../posts/20250731-artin-noether/">上篇</a>中对零维 Noether 环的结构做了详尽的分析，局部情形的主要结果如下： ]]></description>
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  <category>algebra</category>
  <category>commalg</category>
  <guid>https://blog.sun123zxy.top/posts/20260406-dvr-dedekind/</guid>
  <pubDate>Tue, 07 Apr 2026 00:00:00 GMT</pubDate>
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<item>
  <title>Spec，可约与连通性</title>
  <dc:creator>sun123zxy </dc:creator>
  <link>https://blog.sun123zxy.top/posts/20260228-spec-connect/</link>
  <description><![CDATA[ 本文中环均为交换幺环． ]]></description>
  <category>math</category>
  <category>algebra</category>
  <category>commalg</category>
  <guid>https://blog.sun123zxy.top/posts/20260228-spec-connect/</guid>
  <pubDate>Fri, 27 Feb 2026 00:00:00 GMT</pubDate>
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  <title>Comparing Free Modules via Homomorphisms</title>
  <dc:creator>sun123zxy </dc:creator>
  <link>https://blog.sun123zxy.top/posts/20260225-free-module-cmp/</link>
  <description><![CDATA[ We discuss some well-known results that compare finitely-generated free modules via homomorphisms. Let <img src="https://latex.codecogs.com/png.latex?R"> be a nonzero commutative ring with <img src="https://latex.codecogs.com/png.latex?1">. ]]></description>
  <category>math</category>
  <category>algebra</category>
  <category>commalg</category>
  <guid>https://blog.sun123zxy.top/posts/20260225-free-module-cmp/</guid>
  <pubDate>Wed, 25 Feb 2026 00:00:00 GMT</pubDate>
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  <title>Selected solutions to Atiyah-Macdonald’s exercises</title>
  <dc:creator>sun123zxy </dc:creator>
  <link>https://blog.sun123zxy.top/posts/20251218-atiyah/</link>
  <description><![CDATA[ <span class="theorem-title"><strong>Exercise 1 (<span class="citation" data-cites="AM1969">[1]</span>-exr-2.1)</strong></span> <img src="https://latex.codecogs.com/png.latex?%5Cmathbb%20Z%20/%20m%20%5Cmathbb%20Z%20%5Cotimes_%7B%5Cmathbb%20Z%7D%20%5Cmathbb%20Z%20/%20n%20%5Cmathbb%20Z%20=%200"> when <img src="https://latex.codecogs.com/png.latex?m,%20n"> are coprime. ]]></description>
  <category>math</category>
  <category>algebra</category>
  <category>commalg</category>
  <guid>https://blog.sun123zxy.top/posts/20251218-atiyah/</guid>
  <pubDate>Thu, 18 Dec 2025 00:00:00 GMT</pubDate>
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<item>
  <title>零点定理乱炖</title>
  <dc:creator>sun123zxy </dc:creator>
  <link>https://blog.sun123zxy.top/posts/20250709-hnt/</link>
  <description><![CDATA[ 本文所指环均为含幺交换环． ]]></description>
  <category>math</category>
  <category>algebra</category>
  <category>commalg</category>
  <guid>https://blog.sun123zxy.top/posts/20250709-hnt/</guid>
  <pubDate>Tue, 12 Aug 2025 00:00:00 GMT</pubDate>
</item>
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  <title>Artin–Noether 乱炖</title>
  <dc:creator>sun123zxy </dc:creator>
  <link>https://blog.sun123zxy.top/posts/20250731-artin-noether/</link>
  <description><![CDATA[ 本文所指环均为交换幺环．我们重新编排一下 <span class="citation" data-cites="m_f_atiyah_introduction_1969">[1, chapter 8]</span> 的顺序，开发以下著名的 Artin 环等价刻画的证明： ]]></description>
  <category>math</category>
  <category>algebra</category>
  <category>commalg</category>
  <guid>https://blog.sun123zxy.top/posts/20250731-artin-noether/</guid>
  <pubDate>Fri, 01 Aug 2025 00:00:00 GMT</pubDate>
  <media:content url="https://blog.sun123zxy.top/listings/commalg/am69.jpg" medium="image" type="image/jpeg"/>
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<item>
  <title>On Determining Prime Spectra of Some Coordinate Rings</title>
  <dc:creator>sun123zxy </dc:creator>
  <link>https://blog.sun123zxy.top/posts/20250509-spec/</link>
  <description><![CDATA[ In this article, all rings are commutative with <img src="https://latex.codecogs.com/png.latex?1"> unless otherwise specified. <span class="citation" data-cites="atiyah_commalg">[1]</span> is referred for terms not defined here. ]]></description>
  <category>math</category>
  <category>algebra</category>
  <category>commalg</category>
  <guid>https://blog.sun123zxy.top/posts/20250509-spec/</guid>
  <pubDate>Fri, 16 May 2025 00:00:00 GMT</pubDate>
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