Characterizing Cohen-Macaulay local rings by Frobenius maps

Ryo Takahashi, Yuji Yoshino

Research output: Contribution to journalArticle

9 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 languageEnglish
Pages (from-to)3177-3187
Number of pages11
JournalProceedings of the American Mathematical Society
Volume132
Issue number11
DOIs
Publication statusPublished - Nov 1 2004

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Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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