On graded hyperrings and graded hypermodules

Document Type: Research Paper


Department of Mathematics, Payame Noor University (PNU), P.O.BOX 19395-3697 Tehran, Iran,



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.


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