On S-prime hyperideals in multiplicative hyperrings

Let R be a multiplicative hyperring and S ⊆ R be a multiplicatively closed subset of R. In this paper, we introduce and study the concept of S-prime hyperide-als which is a generalization of prime hyperideals. Some properties of S-prime hyperideals in multiplicative hyper-ring are presented. Then we investigate the behaviour of S-prime hyperideals under homomorphism hyperrings, in factor hyperrings, Cartesian products of hyperrings, and the fundamental relation in the context of multiplicative hyperring.