A generalization of a theorem of Foxby
Commutative Algebra
2009-04-03 v2 Rings and Algebras
Abstract
In this paper, it is proved that a commutative noetherian local ring admitting a finitely generated module of finite projective and injective dimensions with respect to a semidualizing module is Gorenstein. This result recovers a celebrated theorem of Foxby.
Cite
@article{arxiv.0902.3037,
title = {A generalization of a theorem of Foxby},
author = {Tokuji Araya and Ryo Takahashi},
journal= {arXiv preprint arXiv:0902.3037},
year = {2009}
}
Comments
4 pages, the proof of Lemma 2.1 is shortened, to appear in Arch. Math. (Basel)