https://commalg.subwiki.org/w/index.php?action=history&feed=atom&title=Projective_dimension_of_a_module 2026-09-20T02:33:41Z Revision history for this page on the wiki MediaWiki 1.41.2 https://commalg.subwiki.org/w/index.php?title=Projective_dimension_of_a_module&diff=1046&oldid=prev 2008-05-12T16:33:42Z

<p>2 revisions</p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <tr class="diff-title" lang="en"> <td colspan="1" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="1" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 16:33, 12 May 2008</td> </tr><tr><td colspan="2" class="diff-notice" lang="en"><div class="mw-diff-empty">(No difference)</div> </td></tr></table>

Vipul https://commalg.subwiki.org/w/index.php?title=Projective_dimension_of_a_module&diff=1045&oldid=prev 2007-08-21T03:21:36Z

<p><span dir="auto"><span class="autocomment">Related notions</span></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 03:21, 21 August 2007</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l8">Line 8:</td> <td colspan="2" class="diff-lineno">Line 8:</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>* [[Injective dimension of a module]]</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>* [[Injective dimension of a module]]</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;">Projective </del>dimension of a ring]]</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;">Global </ins>dimension of a ring]]</div></td></tr> </table>

Vipul https://commalg.subwiki.org/w/index.php?title=Projective_dimension_of_a_module&diff=1044&oldid=prev 2007-08-21T03:19:39Z

<p></p> <p><b>New page</b></p><div>==Definition==<br /> <br /> ===Symbol-free definition===<br /> <br /> The &#039;&#039;&#039;projective dimension&#039;&#039;&#039; of a [[module]] over a [[commutative unital ring]] is defined as the minimum of the lengths of finite [[projective resolution]]s of the module (here, the length is the number of members apart from the module itself and zero). If there is no projective resolution of finite length, the projective dimension is taken as &lt;math&gt;\infty&lt;/math&gt;.<br /> <br /> ==Related notions==<br /> <br /> * [[Injective dimension of a module]]<br /> * [[Projective dimension of a ring]]</div>

Vipul