A new version of P-flat modules and its applications

TL;DR

This paper introduces $$-$w$-P-flat modules, a new generalized class that unifies previous concepts and has applications in characterizing certain ring properties.

Contribution

It defines and studies $$-$w$-P-flat modules, showing they form a covering class and can characterize various $$-ring structures.

Findings

$$-$w$-P-flat modules form a covering class.

Characterization of $$-von Neumann regular rings.

Application to strong $$-rings and $$-PvMRs.

Abstract

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.