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arXiv · 1412.8046

Maximal Cohen-Macaulay approximations and Serre's condition

Hiroki Matsui·Ryo Takahashi
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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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Hiroki Matsui, Ryo Takahashi. 2014-12-27. Maximal Cohen-Macaulay approximations and Serre's condition. https://arxiv.org/abs/1412.8046

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