on graded hyperrings and graded hypermodules

Let g be a monoid with identity e. in this paper, first we introduce the notions of g-graded hyperrings, graded hyperideals and graded hyperfields in the sense of krasner hyperring r. also, we define the notion of a greded r-hypermodules and some examples are presented. then we investigate graded maximal, graded prime and graded primary hyperideals of a graded hyperring r. finally, we study graded maximal, graded prime and graded primary subhypermodules of a graded r-hypermodule m and some interesting results on these concepts are given.