https://commalg.subwiki.org/w/index.php?action=history&feed=atom&title=Depth_of_an_ideal 2026-10-08T15:52:50Z Revision history for this page on the wiki MediaWiki 1.41.2 https://commalg.subwiki.org/w/index.php?title=Depth_of_an_ideal&diff=204&oldid=prev 2008-05-12T16:19:36Z

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Vipul https://commalg.subwiki.org/w/index.php?title=Depth_of_an_ideal&diff=203&oldid=prev 2008-03-09T19:30:26Z

<p>New page: ==Definition== Let &lt;math&gt;R&lt;/math&gt; be a <a href="/wiki/Commutative_unital_ring" title="Commutative unital ring">commutative unital ring</a> and &lt;math&gt;I&lt;/math&gt; be an <a href="/wiki/Ideal" title="Ideal">ideal</a> inside &lt;math&gt;R&lt;/math&gt;. The &#039;&#039;&#039;depth&#039;&#039;&#039; of &lt;math&gt;I&lt;/math&gt; is the length of a maximal [...</p> <p><b>New page</b></p><div>==Definition==<br /> <br /> Let &lt;math&gt;R&lt;/math&gt; be a [[commutative unital ring]] and &lt;math&gt;I&lt;/math&gt; be an [[ideal]] inside &lt;math&gt;R&lt;/math&gt;. The &#039;&#039;&#039;depth&#039;&#039;&#039; of &lt;math&gt;I&lt;/math&gt; is the length of a maximal [[regular sequence]] in &lt;math&gt;I&lt;/math&gt;. A regular sequence is a sequence of elements where each element is &#039;&#039;not&#039;&#039; a zero divisor in the ideal spanned by the preceding elements.<br /> <br /> A related notion is [[depth of an ideal on a module]], where we replace &#039;&#039;zero divisor&#039;&#039; by &#039;&#039;zero divisor on the module&#039;&#039;.</div>

Vipul