A generalization of a theorem of Foxby

2009/02/18 by Araya, Tokuji, Takahashi, Ryo
#13C13 #13D05 #13H10 #Commutative Algebra (math.AC) #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/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.

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