2021/02/15 by Khashan, Hani A., Celikel, Ece Yetkin · 1 citation
#13A15 #13A18 #13A99 #Commutative Algebra (math.AC) #FOS: Mathematics
paper · doi:10.48550/arxiv.2102.07823
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 a∈ 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.