Weakly S-2-prime ideals of commutative rings

Abstract

The objective of this paper is to introduce and investigate the concept of weakly S-2-prime ideals which are extensions of weakly 2-prime ideals in commutative rings. Let R be a commutative ring with identity and S be a multiplicative subset of R with 1 ∈ S. A proper ideal Q of R with Q ∩ S = ∅ is called a weakly S-2-prime ideal of R if there exists an s ∈ S such that for all α, β ∈ R with 0 ≠ αβ ∈ Q, we have sα2 ∈ Q or sβ2 ∈ Q. Various characterizations of weakly S-2-prime ideals are given and the relationship between weakly S-2-prime ideals and other classical ideals are illustrated by a diagram. For this relationship, a myriad of supporting examples and counter examples are presented. Moreover, this class of ideals is analyzed in idealization rings and amalgamated duplication along an ideal. Besides, the rings over which every weakly S-2-prime ideal is S-2-prime ideal is examined. © 2025, Sidi Mohamed Ben Abdellah University. All rights reserved.