Weakly J-ideals of commutative rings

Abstract

Let R be a commutative ring with non-zero identity. In this pa-
per, 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 2 R with 0 6= ab 2 I and a =2 J(R), then a 2 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 amagamated ring along an ideal.