In this paper, we introduce and study the class of φ-w-P-flat modules, which can be seen as generalizations of both φ-P-flat modules and w-P-flat modules. In particular, we obtain that the class of φ-w-P-flat modules is covering. We also utilize the class of φ-w-P-flat modules to characterize φ-von Neumann regular rings, strong φ-rings and φ-PvMRs.
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Wei et al. (2024) studied this question.
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