α-Prime Hyperideals in a Multiplicative Hyperring

The notion of multiplicative hyperrings is an important class of algebraic hyperstructures which generalize rings where the multiplication is a hyperoperation, while the addition is an operation . Let R be a commutative multiplicative hyperring and α ∈ End(R). A proper hyperideal I of R is called α-prime if x ◦ y ⊆ I for some x, y ∈ R then x ∈ I or α(y) ∈ I. Indeed, the α-prime hyperideals are a new generalization of prime hyperideals. In this paper, we aim to study α-prime hyperideals and give the basic properties of this new type of hyperideals.