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

Abstract

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 $s \in R$ and $x\in M$ such that $sx=0$. In this paper, we introduce and study the class of $\phi$-PF-rings, i.e., rings in which all ideals are $\phi$-P-flat. Among other results, the transfer of the $\phi$-PF-ring to the amalgamation is investigated. Several examples which delineate the concepts and results are provided.