r-Subhypermodules over Krasner Hypermodules

Abstract

In this study, we introduce the notion ofr-subhypermodule of anR-hypermodule, whereRis a commutative Krasner hyperring. A proper subhypermoduleNofMis said to be anr-subhypermodule ifa·m∈NwithannM(a) =0Mimplies thatm∈Nfor eacha∈ R,m∈M. Weinvestigate the relations between the concept of prime subhypermodules andr-subhypermodules.We also give some results aboutr-subhypermodules.