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EXISTENCE OF ALMOST SPLIT SEQUENCES VIA REGULAR SEQUENCES

Part of: Representation theory of rings and algebras

Published online by Cambridge University Press:  18 March 2013

HOSSEIN ESHRAGHI
HOSSEIN ESHRAGHI*
Affiliation:
Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Kashan, PO Box 87317-51167, Kashan, Iran email eshraghi@kashanu.ac.ir
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Abstract

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Let $(R, \mathfrak{m})$ be a Cohen–Macaulay complete local ring. We will apply an inductive argument to show that for every nonprojective locally projective maximal Cohen–Macaulay object $ \mathcal{X} $ of the morphism category of $R$ with local endomorphism ring, there exists an almost split sequence ending in $ \mathcal{X} $. 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 is described.

Keywords

almost split sequenceCohen–Macaulay modulesmorphism category

MSC classification

Secondary: 16G70: Auslander-Reiten sequences (almost split sequences) and Auslander-Reiten quivers 16G50: Cohen-Macaulay modules
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 88 , Issue 2 , October 2013 , pp. 218 - 231
Copyright
Copyright ©2013 Australian Mathematical Publishing Association Inc. 

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