Ding projective and Ding injective modules over trivial ring extensions

Abstract

We introduce the concepts of generalized compatible and cocompatible bimodules in order to characterize Gorenstein projective, injective and flat modules over trivial ring extensions. Let R ⋉ M be a trivial extension of a ring R by→ X is exact and coker(α) is a Gorenstein projective left R-module. Analogously, we explicitly characterize Gorenstein injective and flat modules over trivial ring extensions. As an application, we describe Gorenstein projective, injective and flat modules over Morita context rings with zero bimodule homomorphisms.