On expansions of graded 2-absorbing hyperideals in graded multiplicative hyperrings

Abstract

Let G be an abelian group with identity e. Let R be a graded multiplicative hyperring and ? : Igr(R) ? Igr(R) be an expansion function of Igr(R), where Igr(R) is the set of all graded hyperideals of R. In this paper, we introduce and study the concepts of graded ?-primary hyperideals of R and graded 2-absorbing ?-primary hyperideals of R which are the extended classes of graded prime and graded 2- absorbing hyperideals of R, respectively. Moreover, we give the basic properties of these new types of graded hyperideals and investigate the relations among these structures.