2021/02/20 by Hani A. Khashan, Khashan, Hani A., Ece Yetki̇n Çeli̇kel +1 · 1 citation
Mathematics · #13A15 #13A18 #13A99 #Advanced Topics in Algebra #Commutative Algebra (math.AC) #FOS: Mathematics #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2102.10299
openalex publication_date 2021/02/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let R be a commutative ring with identity. In this paper, we introduce the concept of quasi J-ideal which is a generalization of J-ideal. A proper ideal of R is called a quasi J-ideal if its radical is a J-ideal. Many characterizations of quasi J-ideals in some special rings are obtained. We characterize rings in which every proper ideal is quasi J-ideal. Further, as a generalization of presimplifiable rings, we define the notion of quasi presimplifiable rings. We call a ring R a quasi presimplifiable ring if whenever a,b∈ R and a=ab, then either a is a nilpotent or b is a unit. It is shown that a proper ideal I that is contained in the Jacobson radical is a quasi J-ideal (resp. J-ideal) if and only if R/I is a quasi presimplifiable (resp. presimplifiable) ring.