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.
Acknowledgments
I thank Dr. P. Dheena, Professor, Department of Mathematics, Annamalai University, for suggesting the problem and going through the proof.
Citation
Govindarajulu Narayanan Sudharshana. Duraisamy Sivakumar. "$\boldsymbol{R}$-regular modules." Missouri J. Math. Sci. 35 (1) 75 - 84, May 2023. https://doi.org/10.35834/2023/3501075
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