A generalization of a theorem of Foxby
arXiv:0902.3037
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.
4 pages, the proof of Lemma 2.1 is shortened, to appear in Arch. Math. (Basel)