r-Subhypermodules over Krasner hypermodules

Abstract

In this study, we introduce the notion of r-subhypermodule of an 1Z-hypermodule, where 1Z is a commutative Krasner hyperring. A proper subhypermodule N of M is said to be an r-subhypermodule if a m E N with annM(a) = 0M implies that m E N for each a E 1Z, m E M. We investigate the relations between the concept of prime subhypermodules and r-subhypermodules. We also give some results about r-subhypermodules.