Gorenstein projective modules over rings of Morita contexts

Under semi-weak and weak compatibility conditions of bimodules,we establish necessary and sufficient conditions of Gorenstein-projective modules over rings of Morita contexts with one bimodule homomorphism zero.This extends greatly the 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.Our results are proved under a general setting of noetherian rings and modules instead of Artin algebras and modules.