Finite homological dimension and primes associated to integrally closed ideals

Authors:
Shiro Goto and Futoshi Hayasaka

Journal:
Proc. Amer. Math. Soc. **130** (2002), 3159-3164

MSC (2000):
Primary 13H05; Secondary 13H10

Published electronically:
March 14, 2002

MathSciNet review:
1912992

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be an integrally closed ideal in a commutative Noetherian ring . Then the local ring is regular (resp. Gorenstein) for every if the projective dimension of is finite (resp. the Gorenstein dimension of is finite and satisfies Serre's condition (S)).

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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:
https://doi.org/10.1090/S0002-9939-02-06436-5

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

Published electronically:
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

Article copyright:
© Copyright 2002
American Mathematical Society