$\boldsymbol{R}$-regular modules

Abstract

The notion of $R$-regular module is introduced. We will show that if $M$ is a torsion-free module over a commutative ring, then $M$ is $R$-regular module if and only if $M$ is a strongly regular module. We will also show that if $M$ is a cyclic $R$-regular $IFP$ module, then the submodule $P$ is completely prime if and only if $P$ is maximal.