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Finite homological dimension and primes associated to integrally closed ideals

Author(s): Shiro Goto; Futoshi Hayasaka
Journal: Proc. Amer. Math. Soc. 130 (2002), 3159-3164.
MSC (2000): Primary 13H05; Secondary 13H10
Posted: March 14, 2002
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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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Additional Information:

Shiro Goto
Affiliation: Department of Mathematics, School of Science and Technology, Meiji University, 214-8571 Japan
Email: goto@math.meiji.ac.jp

Futoshi Hayasaka
Affiliation: Department of Mathematics, School of Science and Technology, Meiji University, 214-8571 Japan
Email: ee68048@math.meiji.ac.jp

DOI: 10.1090/S0002-9939-02-06436-5
PII: S 0002-9939(02)06436-5
Keywords: Projective dimension, Gorenstein dimension, integrally closed ideal, $\mathfrak{m}$-full ideal, regular local ring, Gorenstein local ring
Received by editor(s): January 1, 2001
Received by editor(s) in revised form: June 8, 2001
Posted: March 14, 2002
Additional Notes: The first author was supported by the Grant-in-Aid for Scientific Researches in Japan (C(2), No. 13640044).
Communicated by: Wolmer V. Vasconcelos
Copyright of article: Copyright 2002, American Mathematical Society

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