ON STRONGLY S-PRIME IDEALS

Let R be a commutative ring with identity and S ⊆ R a multiplicative subset. In this paper we introduce the concept of strongly S-prime ideals which is a generalization of prime ideals. Let P be an ideal of R disjoint with S. We say that P is an strongly S-prime ideal of R if for all a, b ∈ R if ab ∈ P, then there exists s ∈ S such that sa ∈ P or sb ∈ P