Dualizing modules and n-perfect rings

Abstract

In this article we extend the results about Gorenstein modules and Foxby duality to a noncommutative setting. This is done in § 3 of the paper, where we characterize the Auslander and Bass classes which arise whenever we have a dualizing module associated with a pair of rings. In this situation it is known that flat modules have finite projective dimension. Since this property of a ring is of interest in its own right, we devote § 2 of the paper to a consideration of such rings. Finally, in the paper's final section, we consider a natural generalization of the notions of Gorenstein modules which arises when we are in the situation of § 3, i.e. when we have a dualizing module.