Proceedings of the American Mathematical Society

Author(s): Ryo Takahashi; Yuji Yoshino
Journal: Proc. Amer. Math. Soc. 132 (2004), 3177-3187.
MSC (2000): Primary 13A35, 13D05, 13H10
Posted: May 12, 2004
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Abstract: Let

be a commutative noetherian local ring of prime characteristic. Denote by ${{}^e\hspace{-1.6pt}{}} R$ the ring

regarded as an

-algebra through

-times composition of the Frobenius map. Suppose that

is F-finite, i.e., ${{}^1\hspace{-2pt}{}} R$ is a finitely generated

-module. We prove that

is Cohen-Macaulay if and only if the

-modules ${{}^e\hspace{-1.6pt}{}} R$ have finite Cohen-Macaulay dimensions for infinitely many integers

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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

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