ON φ-VON NEUMANN REGULAR RINGS

Abstract

Let R be a commutative ring with <TEX>$1{\neq}0$</TEX> and let <TEX>$\mathcal{H}$</TEX> = {R|R is a commutative ring and Nil(R) is a divided prime ideal}. If <TEX>$R{\in}\mathcal{H}$</TEX>, then R is called a <TEX>${\phi}$</TEX>-ring. In this paper, we introduce the concepts of <TEX>${\phi}$</TEX>-torsion modules, <TEX>${\phi}$</TEX>-flat modules, and <TEX>${\phi}$</TEX>-von Neumann regular rings.