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