Gorenstein-Projective Modules over a Class of Morita Rings

Abstract

Let ${\mathrm{\Delta }}_{\left(\mathrm{0,0}\right)}=\left[\begin{array}{cc}A& A{N}_B\\ B{M}_A& B\end{array}\right]$ be a Morita ring such that the bimodule homomorphisms are zero. In this paper, we give sufficient conditions for a ${\mathrm{\Delta }}_{\left(\mathrm{0,0}\right)}$ -module $\left(X,Y,f,g\right)$ to be Gorenstein-projective. As an application, we give sufficient conditions when the algebras $A$ and $B$ inherit the strongly CM-freeness of ${\mathrm{\Delta }}_{\left(\mathrm{0,0}\right)}$ .