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

 

Regular sequences, projective dimension and criteria for regularity of local rings


Authors: P. Jothilingam and S. Mangayarcarassy
Journal: Proc. Amer. Math. Soc. 120 (1994), 1017-1019
MSC: Primary 13H05; Secondary 13D05
MathSciNet review: 1170546
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Abstract: Foxby proves the following proposition (Math. Z. 132 (1973)). Let $ (R,\mathfrak{m})$ be a noetherian local ring and $ M$ any finitely generated $ R$-module such that the projective dimension of $ M/\mathfrak{a}M$ is finite for all ideals $ \mathfrak{a}$ of finite projective dimension. Then either $ M$ is free or $ R$ is regular local. In this article we prove that the conclusion holds if we restrict only to ideals generated by regular sequences, with the empty sequence being interpreted as the zero ideal.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1994-1170546-7
PII: S 0002-9939(1994)1170546-7
Keywords: Projective dimension, regular rings, regular sequence, discrete valuation ring
Article copyright: © Copyright 1994 American Mathematical Society