On 3-absorbing Hyperideals of Multiplicative Hyperring

Abstract

Let $R$ be a multiplicative hyperring. In this research, we learn 3-absorbing hyperideal which is an extension of prime hyperideal. A non zero hyperideal $ J $ of a multiplicative hyperring $ R $ is called a 3-absorbing hyperideal of $ R $ if whenever $ x, y, z, w \in Q $ and $ x\cdot y\cdot z\cdot w\cdot \in J ,$ then either $ x\cdot y\cdot\cdot z \in J $ or $ y\cdot z\cdot w \in J $ or $ x\cdot z \cdot w \in J $ or $ x\cdot y\cdot w \in J $. A number of results concerning 3-absorbing hyperideals and examples of 3-absorbing primary ideals are given.