Modules that detect finite homological dimensions
Commutative Algebra
2015-11-03 v2 Representation Theory
Abstract
We study homological properties of test modules that are, in principle, modules that detect finite homological dimensions. The main outcome of our results is a generalization of a classical theorem of Auslander and Bridger: we prove that, if a commutative Noetherian complete local ring R admits a test module of finite Gorenstein dimension, then R is Gorenstein.
Cite
@article{arxiv.1207.5869,
title = {Modules that detect finite homological dimensions},
author = {Olgur Celikbas and Hailong Dao and Ryo Takahashi},
journal= {arXiv preprint arXiv:1207.5869},
year = {2015}
}
Comments
to appear in Kyoto Journal of Mathematics