Weakly S-2-absorbing ideals in non-commutative rings

Abstract

This paper introduces and explores the notion of weakly S-2-absorbing ideals within the framework of non-commutative rings. Extending the concepts of weakly 2-absorbing ideals and weakly S-prime ideals, an ideal K of a ring R, which is disjoint from an m-system S, is defined as a (weakly) S-2-absorbing ideal if, for all r₁, r₂, r₃ ∈ R with r₁Rr₂Rr₃ ⊆ K (or 0 ≠ r₁Rr₂Rr₃ ⊆ K), there exists s ∈ S such that r₁r₂〈s〉 ⊆ K, r₁r₃〈s〉 ⊆ K, or r₂r₃〈s〉 ⊆ K. We investigate key properties of weakly S-2-absorbing ideals, highlighting their differences from related structures such as weakly 2-absorbing ideals. Additionally, we analyze weakly S-2-absorbing ideals in various ring constructions.