Maximal Cohen-Macaulay approximations and Serre's condition

2014/12/27 by Hiroki Matsui, Ryo Takahashi, Matsui, Hiroki +1 · 1 citation
Mathematics · #13C14 #13H10 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1412.8046

openalex publication_date 2014/12/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper studies the relationship between Serre's condition (\R_n) and Auslander--Buchweitz's maximal Cohen--Macaulay approximations. It is proved that a Gorenstein local ring satisfies (\R_n) if and only if every maximal Cohen--Macaulay module is a direct summand of a maximal Cohen--Macaulay approximation of a (Cohen--Macaulay) module of codimension n+1.

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