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A generalization of a theorem of Foxby

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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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Authors and Affiliations

  1. Nara University of Education, Takabatake-cho, Nara, 630-8528, Japan

    Tokuji Araya

  2. Department of Mathematical Sciences, Faculty of Science, Shinshu University, 3-1-1 Asahi, Matsumoto, Nagano, 390-8621, Japan

    Ryo Takahashi

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  1. Tokuji Araya
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  2. Ryo Takahashi
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Correspondence to Tokuji Araya.

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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

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