English

Auslander-Reiten sequences for Gorenstein rings of dimension one

Commutative Algebra 2018-10-22 v2 Representation Theory

Abstract

Let RR be a complete local Gorenstein ring of dimension one, with maximal ideal m. We show that if MM is a Cohen-Macaulay RR-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