On secondary subhypermodules

Abstract

‎Let $R$ be a Krasner hyperring and $M$ be an $R$- hypermodule. Let $psi: S^{h}(M)rightarrow S^{h}(M)cup {emptyset}$ be a function, where $S^{h}(M)$ denote the set of all subhypermodules of $M$.  In the first part of this paper, we introduce the concept of a secondary hypermodule over a Krasner hyperring. A non-zero hypermodule $M$ over a Krasner hyperring $R$ is called secondary if for every $rin R$, $rM=M$ or $r^{n}M=0$ for some positive integer $n$. Then we investigate some basic properties of secondary hypermodules. Second,  we introduce the notion of $psi$-secondary subhypermodules of an $R$-hypermodule and we obtain some properties of such subhypermodules.