Finite homological dimension and primes associated to integrally closed ideals

Goto, Shiro; Hayasaka, Futoshi

doi:10.1090/S0002-9939-02-06436-5

Finite homological dimension and primes associated to integrally closed ideals
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Proc. Amer. Math. Soc. 130 (2002), 3159-3164 Request permission

Abstract:

Let $I$ be an integrally closed ideal in a commutative Noetherian ring $A$. Then the local ring $A_{\mathfrak {p}}$ is regular (resp. Gorenstein) for every $\mathfrak {p} \in \mathrm {Ass}_{A} A/I$ if the projective dimension of $I$ is finite (resp. the Gorenstein dimension of $I$ is finite and $A$ satisfies Serre’s condition (S$_{1}$)).

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