More on the weakly S-2-prime ideals of commutative rings

Abstract

Prime ideals and their generalizations are fundamental in various research areas, especially in commutative algebra. The study of weakly prime ideals is marked the beginning of this generalization. Subsequent research has further expanded these concepts, with recent attention on weakly 2-prime and S-2-prime ideals. This study aims for new characterizations of weakly S-2-prime ideals, a generalization that includes both weakly 2-prime and S-2-prime ideals. To achieve this goal, we construct an ideal disjoint with a multiplicatively closed subset of commutative rings. We explore several characterizations concerning weakly S-2-prime ideals and investigate this class of ideals in polynomial and formal power series rings. Besides, we examine several new results regarding the trivial extension and amalgamated algebra along an ideal with respect to a ring homomorphism concerning weakly S-2-prime ideals.