Serre's criterion for normality
id:
serre-s-criterion-for-normality-304-10048291
title:
Serre's criterion for normality
text:
In algebra, Serre's criterion for normality, introduced by Jean-Pierre Serre, gives necessary and sufficient conditions for a commutative Noetherian ring A to be a normal ring. The criterion involves the following two conditions for A: R k : A p is a regular local ring for any prime ideal p of height ≤ k. S k : depth A p ≥ inf { k , ht } for any prime ideal p . The statement is: A is a reduced ring ⇔ R 0 , S 1 hold.
A is a normal ring ⇔ R 1 , S 2 hold.
A is a Cohen–Macaulay ring ⇔ S k hold f
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https://en.wikipedia.org/wiki/Serre%27s_criterion_for_normality
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date modified:
2023-08-10T14:28:49Z
main entity:
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