More on the weakly 2-prime ideals of commutative rings

Abstract

Let R be a commutative ring with a nonzero identity. In this paper we introduce the concept of weakly 2-prime ideal which is a generalization of 2-prime ideal and both are generalization of prime ideals. A proper ideal I of R is called weakly 2-prime ideal if whenever a,b∈R with 0≠ab∈I, then a² or b² lies in I. A number results concerning weakly 2-prime ideals are given. Furthermore, we characterize the valuation domain and the rings over which every weakly 2-prime ideal is 2-prime and rings over which every weakly 2-prime ideal is semi-primary(i.e √I is a prime ideal). We study the transfer the notion of weakly 2-prime ideal to amalgamted algebras along an ideal A⋈^{f}J.