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 $\delta‎: ‎\mathcal{\mathcal{I}}^{gr}(R) \rightarrow \mathcal{\mathcal{I}}^{gr}(R)}$ be an expansion function of $\mathcal{\mathcal{I}}^{gr}(R)$‎. ‎In this paper‎, ‎we introduce and study the concepts of graded $\delta$-primary hyperideals of $R$ and graded $2$-absorbing $\delta$-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.