Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4584510 | Journal of Algebra | 2015 | 12 Pages |
Abstract
A recent result of Araya asserts that if the Auslander–Reiten conjecture holds in codimension one for a commutative Gorenstein ring R, then it holds for R. This note extends this result to left Gorenstein R-algebras Λ, whenever R is a commutative Gorenstein ring. This, in particular, implies that any finitely generated self-orthogonal Gorenstein projective Λ-module is projective, provided Λ is an isolated singularity and dimR≥2dimR≥2. Also, some examples of bound quiver algebras satisfying the Auslander–Reiten conjecture are presented.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Abdolnaser Bahlekeh, Ali Mahin Fallah, Shokrollah Salarian,