Characterizing Cohen-Macaulay local rings by Frobenius maps
Authors:
Ryo Takahashi and Yuji Yoshino
Journal:
Proc. Amer. Math. Soc. 132 (2004), 3177-3187
MSC (2000):
Primary 13A35, 13D05, 13H10
DOI:
https://doi.org/10.1090/S0002-9939-04-07525-2
Published electronically:
May 12, 2004
MathSciNet review:
2073291
Full-text PDF
Abstract | References | Similar Articles | Additional Information
Abstract: Let be a commutative noetherian local ring of prime characteristic. Denote by
the ring
regarded as an
-algebra through
-times composition of the Frobenius map. Suppose that
is F-finite, i.e.,
is a finitely generated
-module. We prove that
is Cohen-Macaulay if and only if the
-modules
have finite Cohen-Macaulay dimensions for infinitely many integers
.
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Additional Information
Ryo Takahashi
Affiliation:
Graduate School of Natural Science and Technology, Okayama University, Okayama 700-8530, Japan
Address at time of publication:
Faculty of Science, Okayama University, Okayama 700-8530, Japan
Email:
takahasi@math.okayama-u.ac.jp
Yuji Yoshino
Affiliation:
Faculty of Science, Okayama University, Okayama 700-8530, Japan
Email:
yoshino@math.okayama-u.ac.jp
DOI:
https://doi.org/10.1090/S0002-9939-04-07525-2
Keywords:
Frobenius map,
CM-dimension,
G-dimension,
flat dimension,
injective dimension
Received by editor(s):
May 15, 2002
Received by editor(s) in revised form:
April 9, 2003, and August 7, 2003
Published electronically:
May 12, 2004
Communicated by:
Bernd Ulrich
Article copyright:
© Copyright 2004
American Mathematical Society