University of Guilan Journal of Algebra and Related Topics 2345-3931 9 1 2021 06 01 On secondary subhypermodules 143 158 4820 10.22124/jart.2021.18981.1256 EN F. Farzalipour Department of Mathematics, Payame Noor University(PNU), Tehran, Iran. P. Ghiasvand Department of Mathematics, Payame Noor University(PNU), Tehran, Iran. Journal Article 2021 02 21 ‎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 $r\in R$, $rM=M$ 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. https://jart.guilan.ac.ir/article_4820_7eef08b07c390ffaa7aa44254e9dd4b9.pdf