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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Strict local rings


Author: J. Herzog
Journal: Proc. Amer. Math. Soc. 84 (1982), 165-172
MSC: Primary 13D10; Secondary 13E10, 13H10
MathSciNet review: 637161
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Abstract: In this paper we introduce the notion of a strict local ring. A local Cohen-Macaulay ring $ (B,m)$ is called strict if, whenever a local ring $ (A,n)$ specializes by a regular sequence to $ B$, then the associated graded ring $ {\text{g}}{{\text{r}}_n}(A)$ is Cohen-Macaulay. We show that an artinian graded algebra $ B$ is strict if for the graded cotangent module we have $ {T^1}{(B/k,B)_r} = 0{\text{for }}\nu < - 1$. Various examples are considered where this condition holds. In particular, with this method we reprove a result of J. Sally [6].


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DOI: http://dx.doi.org/10.1090/S0002-9939-1982-0637161-4
PII: S 0002-9939(1982)0637161-4
Article copyright: © Copyright 1982 American Mathematical Society