A generalization of a theorem of Foxby

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/225574In 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)Commutative AlgebraRings and Algebras13D05, 13C13, 13H10A generalization of a theorem of Foxbytext