On Graded $2$-absorbing Primary Hyperideals of a Graded Multiplicative Hyperring

Document Type : Research Paper


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


‎Let $G$ be a group with identity $e$ ‎and ‎‎$‎R$ be a multiplicative ‎hyperring‎‎. ‎W‎e introduce and study the notions of graded $2$-absorbing and graded $2$-absorbing primary hyperideals of a graded multiplicative hyperring $R$ which are generalizations of prime ‎hyperideals‎‎. ‎We present basic properties and characterizations of these graded hyperideals and homogeneous components‎. Among various results we prove that ‎the intersection of ‎‎‎two ‎graded‎ prime ‎hyperideals ‎is a‎ ‎graded ‎‎$‎2‎‎$‎-absorbing ‎hyperideal.‎