Cotorsion pairs induced by duality pairs

Abstract

We introduce the notion of a duality pair and demonstrate how the left half of such a pair is“often“ covering and preenveloping. As an application, we generalize a result by Enochs et al. on Auslander and Bass classes, and we prove that the class of Gorenstein injective modules–introduced by Enochs and Jenda–is covering when the ground ring has a dualizing complex. © 2009 Rocky Mountain Mathematics Consortium.