On a conjecture of Auslander and Reiten
Commutative Algebra
2007-05-23 v2 Rings and Algebras
Abstract
In studying Nakayama's 1958 conjecture on rings of infinite dominant dimension, Auslander and Reiten proposed the following generalization: Let Lambda be an Artin algebra and M a Lambda-generator such that Ext^i_Lambda(M,M)=0 for all i \geq 1; then M is projective. This conjecture makes sense for any ring. We establish Auslander and Reiten's conjecture for excellent Cohen--Macaulay normal domains containing the rational numbers, and slightly more generally.
Keywords
Cite
@article{arxiv.math/0305001,
title = {On a conjecture of Auslander and Reiten},
author = {Craig Huneke and Graham Leuschke},
journal= {arXiv preprint arXiv:math/0305001},
year = {2007}
}
Comments
12 pages, minor changes, this version to appear