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

Authors : Hwankoo KIM, Najib MAHDOU, El Houssaine OUBOUHOU

Pages : 708-720

Doi:10.15672/hujms.1148258

View : 97 | Download : 192

Publication Date : 2023-05-30

Article Type : Research Paper

Abstract :Let $R$ be a commutative ring with nonzero identity. An $R$-module $M$ is called $\\phi$-P-flat if $x \\in \\Anninsert ignore into journalissuearticles values(s);M$ 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.
Keywords : \\phi flat, \\phi P flat, \\phi PF ring, PF ring, PN ring, ZN ring, \\phi von Neumann regular ring, trivial extension