Regular sequences, projective dimension and criteria for regularity of local rings
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- by P. Jothilingam and S. Mangayarcarassy PDF
- Proc. Amer. Math. Soc. 120 (1994), 1017-1019 Request permission
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.References
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Additional Information
- © Copyright 1994 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 120 (1994), 1017-1019
- MSC: Primary 13H05; Secondary 13D05
- DOI: https://doi.org/10.1090/S0002-9939-1994-1170546-7
- MathSciNet review: 1170546