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