$\alpha$-prime hyperideals in a multiplicative hyperring
Abstract
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 $\alpha \in End(R)$. A proper hyperideal $I$ of $R$ is called $\alpha$-prime if $x \circ y \subseteq I$ for some $x, y \in R$ then $x \in I$ or $\alpha(y) \in I$. Indeed, the $\alpha$-prime hyperideals are a new generalization of prime hyperideals. In this paper, we aim to study $\alpha$-prime hyperideals and give the basic properties of this new type of hyperideals.
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