$r$-Subhypermodules over Krasner hypermodules

Abstract

In this study, we introduce the notion of $r$-subhypermodule of an $\mathcal{R}$-hypermodule, where $\mathcal{R}$ is a commutative Krasner hyperring. A proper subhypermodule $N$ of $M$ is said to be an $r$-subhypermodule if $a\cdot m\in N$ with $ann_{M}(a)=0_{M}$ implies that $m\in N$ for each $a\in\mathcal{R}$, $m\in M$. We investigate the relations between the concept of prime subhypermodules and $r$-subhypermodules. We also give some results about $r$-subhypermodules.