Weakly J-Ideals of Commutative Rings

Abstract

Let R be a commutative ring with non-zero identity.In this paper, we introduce the concept of weakly J-ideals as a new generalization of J-ideals. We call a proper ideal I of a ring R a weakly J-ideal if whenever a, b is an element of R with 0 not equal ab is an element of I and a is not an element of J(R), then b is an element of I. Many of the basic properties and characterizations of this concept are studied. We investigate weakly J-ideals under various contexts of constructions such as direct products, localizations, homomorphic images. Moreover, a number of examples and results on weakly J-ideals are discussed. Finally, the third section is devoted to the characterizations of these constructions in an amalgamated ring along an ideal.