Gorenstein homological modules over tensor rings

Paper

Abstract

For a tensor ring

, under certain conditions, we characterize the Gorenstein projective modules over

, and prove that a

-module

is Gorenstein projective if and only if

is monomorphic and

is a Gorenstein projective

-module. Gorenstein injective (resp., flat) modules over

are also explicitly described. Moreover, we give a characterization for the coherence of

. Some applications to trivial ring extensions and Morita context rings are given.