On secondary subhypermodules

‎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=۰ 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.

Keywords:

‎Krasner ‎hyperring , ‎ hypermodule‎ , ‎secondary ‎hypermodule , ‎ psi-secondary subhypermodule