Projectively coresolved Gorenstein flat modules over semi-trivial ring extensions

Abstract

We establish necessary and sufficient conditions for modules over a semi-trivial ring extension $R\ltimes_{\Phi}M$ to be projectively coresolved Gorenstein flat. Some applications are given in the Morita context ring $\biggl(\begin{matrix} A&_{A}V_{B}\\_{B}U_{A}&B \end{matrix}\biggr)_{(\varphi,\psi)}$.