A new version of P-flat modules and its applications

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