Gorenstein projective modules over rings of Morita contexts

Abstract

By introducing semi-weak and weak compatibility of modules, 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 modules. An application is provided to construct 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.