On phi-2-Absorbing phi‎-2-Absorbing Primary Hyperideals of A Multiplicative Hyperring - Mahdi Anbarloei (Journal of the Indonesian Mathematical Society, 2019)
‎Let $R$ be a multiplicative hyperring‎. ‎In this paper‎, ‎we extend the concept of 2-absorbing hyperideals and 2-absorbing primary hyperideals to the context ‎$‎φ‎$‎-2-absorbing hyperideals and ‎$‎φ‎$‎-2-absorbing primary hyperideals. Let ‎$‎E(R)‎$‎ be the set of hyperideals of ‎$‎R‎$‎‎ and ‎$φ : E(R) \longrightarrow E(R) \cup \{φ\}‎$‎ be a function. A nonzero proper hyperideal ‎$‎I‎$‎ of ‎$‎R‎$‎ is called a ‎$φ‎$‎- 2-absorbing hyperideal if for all ‎$x, y, z \in R, xoyoz \subseteq I- φ(I)‎$‎ implies‎$xoy \subseteq I‎$‎ or ‎$‎yoz \subseteq I‎$‎ or ‎$‎xoz \subseteq I‎$‎. Also, a nonzero proper hyperideal ‎$‎I‎$‎ of ‎$‎R‎$‎ is called a ‎$φ‎$‎- 2-absorbing primary hyperideal if for all ‎$x, y, z \in R, \ xoyoz \subseteq I- φ(I)‎$‎ implies‎$xoy \subseteq I‎$‎ or ‎$‎yoz \subseteq r(I)‎$‎ or ‎$‎xoz \subseteq r(I)‎$‎. A number of results concerning them are given.