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.