On the existence of embeddings into modules of finite homological dimensions
Commutative Algebra
2010-04-05 v3 Rings and Algebras
Abstract
Let R be a commutative Noetherian local ring. We show that R is Gorenstein if and only if every finitely generated R-module can be embedded in a finitely generated R-module of finite projective dimension. This extends a result of Auslander and Bridger to rings of higher Krull dimension, and it also improves a result due to Foxby where the ring is assumed to be Cohen-Macaulay.
Keywords
Cite
@article{arxiv.0811.4461,
title = {On the existence of embeddings into modules of finite homological dimensions},
author = {Ryo Takahashi and Siamak Yassemi and Yuji Yoshino},
journal= {arXiv preprint arXiv:0811.4461},
year = {2010}
}
Comments
4 pages, final version, to appear in Proc. Amer. Math. Soc