https://commalg.subwiki.org/w/index.php?action=history&feed=atom&title=Reduced_Noetherian_one-dimensional_implies_Cohen-MacaulayReduced Noetherian one-dimensional implies Cohen-Macaulay - Revision history2026-08-24T18:13:07ZRevision history for this page on the wikiMediaWiki 1.41.2https://commalg.subwiki.org/w/index.php?title=Reduced_Noetherian_one-dimensional_implies_Cohen-Macaulay&diff=1104&oldid=prevVipul: 1 revision2008-05-12T16:34:04Z<p>1 revision</p>
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</td></tr></table>Vipulhttps://commalg.subwiki.org/w/index.php?title=Reduced_Noetherian_one-dimensional_implies_Cohen-Macaulay&diff=1103&oldid=prevVipul: New page: ==Statement== ===Verbal statement=== A reduced Noetherian one-dimensional ring is Cohen-Macaulay. ==Definitions used== ...2008-05-05T20:11:28Z<p>New page: ==Statement== ===Verbal statement=== A <a href="/wiki/Reduced_ring" title="Reduced ring">reduced</a> <a href="/wiki/Noetherian_ring" title="Noetherian ring">Noetherian</a> <a href="/wiki/One-dimensional_ring" title="One-dimensional ring">one-dimensional ring</a> is <a href="/wiki/Cohen-Macaulay_ring" title="Cohen-Macaulay ring">Cohen-Macaulay</a>. ==Definitions used== ...</p>
<p><b>New page</b></p><div>==Statement==<br />
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===Verbal statement===<br />
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A [[reduced ring|reduced]] [[Noetherian ring|Noetherian]] [[one-dimensional ring]] is [[Cohen-Macaulay ring|Cohen-Macaulay]].<br />
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==Definitions used==<br />
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===Noetherian ring===<br />
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{{further|[[Noetherian ring]]}}<br />
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A [[commutative unital ring]] is termed Noetherian if every ideal in it is finitely generated.<br />
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===Reduced ring===<br />
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{{further|[[reduced ring]]}}<br />
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A [[commutative unital ring]] is termed reduced if it has no nonzero nilpotent element, i.e. its [[nilradical]] is zero. In other words, the intersection of all prime ideals is zero.<br />
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For a Noetherian ring, this is equivalent to demanding that the intersection of all the minimal primes equals zero.<br />
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===One-dimensional ring===</div>Vipul