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2007 Foxby equivalence over associative rings
Henrik Holm, Diana White
J. Math. Kyoto Univ. 47(4): 781-808 (2007). DOI: 10.1215/kjm/1250692289


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.


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Henrik Holm. Diana White. "Foxby equivalence over associative rings." J. Math. Kyoto Univ. 47 (4) 781 - 808, 2007.


Published: 2007
First available in Project Euclid: 19 August 2009

zbMATH: 1154.16007
MathSciNet: MR2413065
Digital Object Identifier: 10.1215/kjm/1250692289

Primary: 16Exx

Rights: Copyright © 2007 Kyoto University

Vol.47 • No. 4 • 2007
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