On S-prime hyperideals in multiplicative hyperrings

Abstract

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 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.

2‐Prime Hyperideals of Multiplicative Hyperrings

“…Then we have y + z ∈ U (A). By Lemma 2.6 in [28], we get the result that A is local which is a contradiction. Thus Q is a (u − 1, v − 1)-absorbing prime hyperideal of A.…”

“…In this hyperstructure, the multiplication is a hyperoperation, while the addition is an operation. Many illustrations and results of the multiplicative hyperring can be seen in [3,4,6,7,8,22,28].…”

“…In this hyperstructure, the multiplication is a hyperoperation however the addition is an operation. Multiplicative hyperrings are deeply demonstrated and characterized in [3,4,5,22,28,29,31,35]. Dasgupta studied the prime and primary hyperideals in multiplicative hyperrings in [17].…”