Farzalipour, Farkhonde; Ghiasvand, Peyman On graded hyperrings and graded hypermodules. (English) Zbl 07260091 Algebr. Struct. Appl. 7, No. 2, 15-28 (2020). 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 Keywords:hyperring; hypermodule; graded hyperring; graded hypermodule PDF BibTeX XML Cite \textit{F. Farzalipour} and \textit{P. Ghiasvand}, Algebr. Struct. Appl. 7, No. 2, 15--28 (2020; Zbl 07260091) Full Text: DOI