Weakly J-ideals of commutative rings

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 ? R with 0 ? ab ? I and a ? J(R), then b ? 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.