https://commalg.subwiki.org/w/index.php?action=history&feed=atom&title=Generalized_local_ring 2026-06-25T01:22:48Z Revision history for this page on the wiki MediaWiki 1.41.2 https://commalg.subwiki.org/w/index.php?title=Generalized_local_ring&diff=1745&oldid=prev 2009-01-03T19:14:11Z

<p><span dir="auto"><span class="autocomment">Stronger properties: </span> multivariate link</span></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 19:14, 3 January 2009</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l15">Line 15:</td> <td colspan="2" class="diff-lineno">Line 15:</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>===Stronger properties===</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>===Stronger properties===</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" 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;">Polynomial </del>ring over a field]]</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;">Multivariate polynomial </ins>ring over a field]]</div></td></tr> </table>

Masnevets https://commalg.subwiki.org/w/index.php?title=Generalized_local_ring&diff=1739&oldid=prev 2009-01-03T18:44:04Z

<p>formatting</p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 18:44, 3 January 2009</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l5">Line 5:</td> <td colspan="2" class="diff-lineno">Line 5:</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>A [[graded ring|positively graded]] [[commutative unital ring]] &#039;&#039;R&#039;&#039; is termed a &#039;&#039;&#039;generalized local ring&#039;&#039;&#039; if its degree 0 part is [[local ring|local]] and [[Noetherian ring|Noetherian]], and &#039;&#039;R&#039;&#039; is a finitely generated as an algebra over its degree 0 part.</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>A [[graded ring|positively graded]] [[commutative unital ring]] &#039;&#039;R&#039;&#039; is termed a &#039;&#039;&#039;generalized local ring&#039;&#039;&#039; if its degree 0 part is [[local ring|local]] and [[Noetherian ring|Noetherian]], and &#039;&#039;R&#039;&#039; is a finitely generated as an algebra over its degree 0 part.</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" 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;">=</del>==Metaproperties<del style="font-weight: bold; text-decoration: none;">=</del>==</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>==Metaproperties==</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" 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>==Uniqueness of maximal ideal==</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;">=</ins>==Uniqueness of maximal ideal<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;"><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>A generalized local ring has a unique maximal homogeneous ideal.</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>A generalized local ring has a unique maximal homogeneous ideal.</div></td></tr> </table>

Masnevets https://commalg.subwiki.org/w/index.php?title=Generalized_local_ring&diff=1738&oldid=prev 2009-01-03T18:41:56Z

<p>New page: ==Definition== ===Symbol-free definition=== A <a href="/wiki/Graded_ring" title="Graded ring">positively graded</a> <a href="/wiki/Commutative_unital_ring" title="Commutative unital ring">commutative unital ring</a> &#039;&#039;R&#039;&#039; is termed a &#039;&#039;&#039;generalized local ring&#039;&#039;&#039; if its degree 0 part is [[local...</p> <p><b>New page</b></p><div>==Definition==<br /> <br /> ===Symbol-free definition===<br /> <br /> A [[graded ring|positively graded]] [[commutative unital ring]] &#039;&#039;R&#039;&#039; is termed a &#039;&#039;&#039;generalized local ring&#039;&#039;&#039; if its degree 0 part is [[local ring|local]] and [[Noetherian ring|Noetherian]], and &#039;&#039;R&#039;&#039; is a finitely generated as an algebra over its degree 0 part.<br /> <br /> ===Metaproperties===<br /> <br /> ==Uniqueness of maximal ideal==<br /> <br /> A generalized local ring has a unique maximal homogeneous ideal.<br /> <br /> ==Relation with other properties==<br /> <br /> ===Stronger properties===<br /> <br /> * [[Polynomial ring over a field]]</div>

Masnevets