Akademik Veri Yönetim Sistemi
Journal of Algebra and its Applications, 2025 (SCI-Expanded, Scopus)
The notion of weakly 2-absorbing ideals, introduced as a natural generalization of prime ideals, has gained significant attention in commutative rings. A weakly 2-absorbing ideal of a commutative ring R ensures that for all a, b, c ∈ R, the inclusion abc /= 0 and abc ∈ I implies that at least one of ab, ac, or bc belongs to I. This paper builds upon the existing framework by introducing and exploring weakly S-2-absorbing ideals in the context of a multiplicatively closed subset S of R. An ideal I, disjoint from S, is defined as weakly S-2-absorbing if abc /= 0 and abc ∈ I guarantee that abs ∈ I, acs ∈ I, or bcs ∈ I for some s ∈ S. We give the fundamental properties of weakly S-2-absorbing ideals and investigate their behavior under various ring constructions, such as amalgamation duplications, homomorphic images, direct products and trivial extensions. Notable results include conditions under which the ideals retain the weakly S-2-absorbing property and characterizations of these ideals in special commutative rings such as reduced rings and local semiprime rings which are not prime.