How to construct Gorenstein projective modules relative to complete duality pairs over Morita rings

Abstract

be a Morita ring with M ⊗ A N = 0 = N ⊗ B M . We first study how to construct (complete) duality pairs of ∆-modules using (complete) duality pairs of A-modules and B-modules, generalizing the result of Mao (Comm. Algebra, 2020, 12: 5296-5310) about the duality pairs over a triangular matrix ring. Moreover, we construct Gorenstein projective modules relative to complete duality pairs of ∆-modules. Finally, we give an application to Ding projective modules.