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

17 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
Externally published	Yes

Keywords

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

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1090/S0002-9939-04-07525-2

Cite this

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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.",

keywords = "CM-dimension, Flat dimension, Frobenius map, G-dimension, Injective dimension",

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T1 - Characterizing Cohen-Macaulay local rings by Frobenius maps

AU - Takahashi, Ryo

AU - Yoshino, Yuji

PY - 2004/11

Y1 - 2004/11

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

UR - https://www.scopus.com/pages/publications/7444223587

UR - https://www.scopus.com/pages/publications/7444223587#tab=citedBy

U2 - 10.1090/S0002-9939-04-07525-2

DO - 10.1090/S0002-9939-04-07525-2

M3 - Article

AN - SCOPUS:7444223587

SN - 0002-9939

VL - 132

SP - 3177

EP - 3187

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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