On Weakly S-Prime Hyperideals of Multiplicative Hyperrings

Let Γ be a commutative with identity multiplicative hyperring and S ⊆ Γ be a multiplicatively closed subset of Γ. In this study, we will discuss the definition and general properties of weakly Γ-prime hyperideals. Let Ω be a hyperideal of Γ disjoint from S. We say that Ω is a weakly S− prime hyperideal of Γ if there exists an s ∈ S such that for all ϱ,σ ∈ Γ , if {0} ̸ = ϱ⋄σ ⊆ Ω then s⋄ϱ ⊆ Ω or s◦y ⊆ Ω . We will also examine the relationship between weakly−S prime hyperideals, weakly prime, and S−prime hyperideals.