Rings that are homologically of minimal multiplicity
Commutative Algebra
2010-01-12 v2
Abstract
Let R be a local Cohen-Macaulay ring with canonical module \omega_R. We investigate the following question of Huneke: If the sequence of Betti numbers \{\beta_i^R(\omega_R)\} has polynomial growth, must R be Gorenstein? This question is well-understood when R has minimal multiplicity. We investigate this question for a more general class of rings which we say are homologically of minimal multiplicity. We provide several characterizations of the rings in this class and establish a general ascent and descent result.
Keywords
Cite
@article{arxiv.0904.3982,
title = {Rings that are homologically of minimal multiplicity},
author = {Keivan Borna and Sean Sather-Wagstaff and Siamak Yassemi},
journal= {arXiv preprint arXiv:0904.3982},
year = {2010}
}
Comments
23 pages, minor revisions for v.2, final version, to appear in Comm. Algebra