Testing for the Gorenstein property
Commutative Algebra
2015-12-31 v3
Abstract
We answer a question of Celikbas, Dao, and Takahashi by establishing the following characterization of Gorenstein rings: a commutative noetherian local ring is Gorenstein if and only if it admits an integrally closed -primary ideal of finite Gorenstein dimension. This is accomplished through a detailed study of certain test complexes. Along the way we construct such a test complex that detect finiteness of Gorenstein dimension, but not that of projective dimension.
Cite
@article{arxiv.1504.08014,
title = {Testing for the Gorenstein property},
author = {Olgur Celikbas and Sean Sather-Wagstaff},
journal= {arXiv preprint arXiv:1504.08014},
year = {2015}
}
Comments
14 pages; v.2 includes minor revisions; v.3 includes some clarifications, minor corrections, a few new examples, and a question