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

Abstract

Let $\Delta =\left(\begin{array}{cc}A& {}_A{N}_B\\ {}_B{M}_A& B\end{array}\right)$ be a Morita ring with $M{\otimes }_{A}N=0=N{\otimes }_{B}M$.We first study how to construct (complete) duality pairs of $\Delta$-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 $\Delta$-modules. Finally, we give an application to Ding projective modules.

18 pages. All comments and suggestions are welcome!