Open AccessWeakly J-ideals of commutative rings
Author(s) -
Hani A. Khashan,
Ece Yetkın Çelıkel
Publication year - 2022
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil2202485k
Subject(s) - mathematics , commutative ring , ideal (ethics) , maximal ideal , generalization , minimal ideal , section (typography) , ring (chemistry) , pure mathematics , identity (music) , primary ideal , commutative property , semiprime ring , fractional ideal , principal ideal ring , discrete mathematics , combinatorics , mathematical analysis , prime (order theory) , law , computer science , chemistry , physics , organic chemistry , political science , acoustics , operating system
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.