Characterizing Cohen-Macaulay local rings by Frobenius maps

Ryo Takahashi; Yuji Yoshino

doi:10.1090/S0002-9939-04-07525-2

Characterizing Cohen-Macaulay local rings by Frobenius maps

Ryo Takahashi, Yuji Yoshino

Research output: Contribution to journal › Article › peer-review

11 Citations (Scopus)

Abstract

Let R be a commutative noetherian local ring of prime characteristic. Denote by ^eR the ring R regarded as an R-algebra through e-times composition of the Frobenius map. Suppose that R is F-finite, i.e., ¹R is a finitely generated R-module. We prove that R is Cohen-Macaulay if and only if the R-modules ^eR have finite Cohen-Macaulay dimensions for infinitely many integers e.

Original language	English
Pages (from-to)	3177-3187
Number of pages	11
Journal	Proceedings of the American Mathematical Society
Volume	132
Issue number	11
DOIs	https://doi.org/10.1090/S0002-9939-04-07525-2
Publication status	Published - Nov 2004

Keywords

CM-dimension
Flat dimension
Frobenius map
G-dimension
Injective dimension

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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10.1090/S0002-9939-04-07525-2

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AU - Takahashi, Ryo

AU - Yoshino, Yuji

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N2 - Let R be a commutative noetherian local ring of prime characteristic. Denote by eR the ring R regarded as an R-algebra through e-times composition of the Frobenius map. Suppose that R is F-finite, i.e., 1R is a finitely generated R-module. We prove that R is Cohen-Macaulay if and only if the R-modules eR have finite Cohen-Macaulay dimensions for infinitely many integers e.

AB - Let R be a commutative noetherian local ring of prime characteristic. Denote by eR the ring R regarded as an R-algebra through e-times composition of the Frobenius map. Suppose that R is F-finite, i.e., 1R is a finitely generated R-module. We prove that R is Cohen-Macaulay if and only if the R-modules eR have finite Cohen-Macaulay dimensions for infinitely many integers e.

KW - CM-dimension

KW - Flat dimension

KW - Frobenius map

KW - G-dimension

KW - Injective dimension

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JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 11

ER -

Characterizing Cohen-Macaulay local rings by Frobenius maps

Abstract

Keywords

ASJC Scopus subject areas

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