Gorenstein projective modules over rings of Morita contexts

TL;DR

This paper characterizes Gorenstein-projective modules over rings of Morita contexts with one zero bimodule homomorphism, extending previous results to more general settings including Noether rings.

Contribution

It provides necessary and sufficient conditions for Gorenstein-projective modules over Morita context rings under weaker compatibility assumptions, broadening the scope of prior work.

Findings

Generalizes results to rings with one bimodule homomorphism zero

Establishes necessary and sufficient conditions for Gorenstein-projective modules

Applies to noncommutative tensor products from Morita contexts

Abstract

Under semi-weak and weak compatibility of bimodules, we establish sufficient and necessary conditions of Gorenstein-projective modules over rings of Morita contexts with one bimodule homomorphism zero. This generalises and extends results on triangular matrix Artin algebras and on Artin algebras of Morita contexts with two bimodule homomorphisms zero in the literature, where only sufficient conditions are given under a strong assumption of compatibility of bimodules. An application is provided to describe Gorenstein-projective modules over noncommutative tensor products arising from Morita contexts. Moreover, we work with Noether rings and modules instead of Artin algebras and modules.