Auslander-Reiten sequences for Gorenstein rings of dimension one
Commutative Algebra
2018-10-22 v2 Representation Theory
Abstract
Let be a complete local Gorenstein ring of dimension one, with maximal ideal m. We show that if is a Cohen-Macaulay -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.
Keywords
Cite
@article{arxiv.1710.00907,
title = {Auslander-Reiten sequences for Gorenstein rings of dimension one},
author = {Robert Roy},
journal= {arXiv preprint arXiv:1710.00907},
year = {2018}
}
Comments
Numerous changes to the presentation, and also one correction: Lemma 6.17 in the new version represents a correction of Lemma 5.19 in the original version