2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/119444We extend the definition of a semidualizing module to 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 in the commutative, noetherian setting.24 pagesCommutative AlgebraRings and Algebras13D02, 13D07, 13D25, 16E05, 16E30text