Journal of Mathematics of Kyoto University

Foxby equivalence over associative rings

Henrik Holm and Diana White

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We extend the definition of a semidualizing module to general associative rings. This enables us to define and study Auslander and Bass classes with respect to a semidualizing bimodule $C$. We then study the classes of $C$-flats, $C$-projectives, and $C$-injectives, and use them to provide a characterization of the modules in the Auslander and Bass classes. We extend Foxby equivalence to this new setting. This paper contains a few results which are new even in the commutative, noetherian setting.

Article information

J. Math. Kyoto Univ., Volume 47, Number 4 (2007), 781-808.

First available in Project Euclid: 19 August 2009

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 16Exx: Homological methods {For commutative rings, see 13Dxx; for general categories, see 18Gxx}


Holm, Henrik; White, Diana. Foxby equivalence over associative rings. J. Math. Kyoto Univ. 47 (2007), no. 4, 781--808. doi:10.1215/kjm/1250692289.

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