Cotorsion pairs induced by duality pairs

TL;DR

This paper introduces duality pairs in module theory, showing their properties and applications, including generalizing known classes and establishing conditions under which Gorenstein injective modules are covering.

Contribution

It defines duality pairs and explores their properties, extending results on Auslander and Bass classes, and proves Gorenstein injective modules are covering over rings with a dualizing complex.

Findings

Duality pairs often have covering and preenveloping properties.

Generalization of Auslander and Bass classes results.

Gorenstein injective modules are covering over rings with a dualizing complex.

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.