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
DOI:
https://doi.org/10.1090/S0002-9939-02-06436-5
Published electronically:
March 14, 2002
MathSciNet review:
1912992
Full-text PDF Free Access
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