On S-prime hyperideals in multiplicative hyperrings

Let R be a multiplicative hyperring and S be a subset of R be a multiplicatively closed subset of R. In this paper, we introduce and study the concept of S-prime hyperideals which is a generalization of prime hyperideals. Some properties of S-prime hyperideals in multiplicative hyperring 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.