English

Auslander-Reiten conjecture and Auslander-Reiten duality

Commutative Algebra 2018-08-21 v3

Abstract

Motivated by a result of Araya, we extend the Auslander-Reiten duality theorem to Cohen-Macaulay local rings. We also study the Auslander-Reiten conjecture, which is rooted in Nakayama's work on finite dimensional algebras. One of our results detects a certain condition that forces the conjecture to hold over local rings of positive depth.

Keywords

Cite

@article{arxiv.1112.6201,
  title  = {Auslander-Reiten conjecture and Auslander-Reiten duality},
  author = {Olgur Celikbas and Ryo Takahashi},
  journal= {arXiv preprint arXiv:1112.6201},
  year   = {2018}
}

Comments

16 pages, to appear in Journal of Algebra