When every ideal is $\phi$-P-flat

Let $R$ be a commutative ring with nonzero identity. An $R$-module $M$ is called $\phi$-P-flat if $x \in \Ann(s)M$ for every non-nilpotent element $s R$ and $x\in M$ such that $sx=0$. In this paper, we introduce study the class of $\phi$-PF-rings, i.e., rings in which all ideals are $\phi$-P-flat. Among other results, transfer $\phi$-PF-ring to amalgamation investigated. Several examples delineate concepts results provided.