A new version of P-flat modules and its applications

Abstract

In this paper, we introduce and study the class of $\ddot{I}•$-$w$-P-flat modules, which can be seen as generalizations of both $\ddot{I}•$-P-flat modules and $w$-P-flat modules. In particular, we obtain that the class of $\ddot{I}•$-$w$-P-flat modules is covering. We also utilize the class of $\ddot{I}•$-$w$-P-flat modules to characterize $\ddot{I}•$-von Neumann regular rings, strong $\ddot{I}•$-rings and $\ddot{I}•$-PvMRs.