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

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.