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On graded hyperrings and graded hypermodules. (English) Zbl 07260091
Summary: 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.
MSC:
20N20 Hypergroups
13A02 Graded rings
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