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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Araya, T., Takahashi, R. A generalization of a theorem of Foxby. Arch. Math. 93, 123–127 (2009). https://doi.org/10.1007/s00013-009-0003-x
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DOI: https://doi.org/10.1007/s00013-009-0003-x