A Class of Abelian Rings
BOLETIN DE MATEMATICAS, vol.25, no.1, pp.27-37, 2018 (ESCI)
- Publication Type: Article / Article
- Volume: 25 Issue: 1
- Publication Date: 2018
- Journal Name: BOLETIN DE MATEMATICAS
- Journal Indexes: Emerging Sources Citation Index (ESCI), Academic Search Premier, Fuente Academica Plus, zbMATH, DIALNET
- Page Numbers: pp.27-37
- Hacettepe University Affiliated: Yes
Abstract
Let R be a ring with identity and J(R) denote the Jacobson radical of R. A ring R is called J-abelian if ae-ea is an element of J(R) for any a is an element of R and any idempotent e in R. In this paper, many characterizations of J-abelian rings are given. We prove that every J-Armendariz ring is J-abelian. We show that the class of J-abelian rings lies strictly between the class of abelian rings and the class of directly finite rings.