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PROGRESS ON THE AUSLANDER–REITEN CONJECTURE

Part of: Local rings and semilocal rings Representation theory of rings and algebras Commutative algebra: Homological methods

Published online by Cambridge University Press:  16 March 2016

ABDOLNASER BAHLEKEH  and
ALI MAHIN FALLAH
ABDOLNASER BAHLEKEH*
Affiliation:
Department of Mathematics, Gonbade-Kavous University, 4971799151, Gonbade-Kavous, Iran email n.bahlekeh@gmail.com
ALI MAHIN FALLAH
Affiliation:
Department of Mathematics, University of Isfahan, PO Box 81746-73441, Isfahan, Iran email amfallah@sci.ui.ac.ir
*
✉n.bahlekeh@gmail.com
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Abstract

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Let $R$ be a commutative Gorenstein ring. A result of Araya reduces the Auslander–Reiten conjecture on the vanishing of self-extensions to the case where $R$ has Krull dimension at most one. In this paper we extend Araya’s result to certain $R$-algebras. As a consequence of our argument, we obtain examples of bound quiver algebras that satisfy the Auslander–Reiten conjecture.

Keywords

Gorenstein ringAuslander–Reiten conjectureGorenstein projective modules

MSC classification

Primary: 13H10: Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.)
Secondary: 16G30: Representations of orders, lattices, algebras over commutative rings 13D02: Syzygies, resolutions, complexes 13D07: Homological functors on modules (Tor, Ext, etc.)
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 93 , Issue 3 , June 2016 , pp. 433 - 440
Copyright
© 2016 Australian Mathematical Publishing Association Inc. 

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