Existence of almost split sequences via regular sequences

Authors

  • H. Eshraghi University of Isfahan

Keywords:

Almost split sequence, Cohen-Macaulay modules, Morphism category

Abstract

Let $(R, \mathfrak{m})$ be a Cohen-Macaulay complete local ring. We will apply an inductive argument to show that for every non-projective locally projective maximal Cohen-Macaulay object $\CX$ of the morphism category of $R$ with local endomorphism ring, there exists an almost split sequence ending in $\CX$. Regular sequences are exploited to reduce the Krull dimension of $R$ on which the inductive argument is established. Moreover, the Auslander-Reiten translate of certain objects are described. 10.1017/S0004972713000099

Published

2013-08-11

Issue

Vol. 88 No. 2 (2013)

Section

Articles
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