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arXiv · 1710.00907

Auslander-Reiten sequences for Gorenstein rings of dimension one

Robert Roy
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Abstract

Let $R$ be a complete local Gorenstein ring of dimension one, with maximal ideal m. We show that if $M$ is a Cohen-Macaulay $R$-module which begins an AR-sequence, then this sequence is produced by a particular endomorphism of m corresponding to a minimal prime ideal. We apply this result to determining the shape of some components of Auslander-Reiten quivers.

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Robert Roy. 2018-10-19. Auslander-Reiten sequences for Gorenstein rings of dimension one. https://arxiv.org/abs/1710.00907

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