A Class of Abelian Rings

HALICIOĞLU S., Harmanci A., ÜNGÖR B.

BOLETIN DE MATEMATICAS, vol.25, no.1, pp.27-37, 2018 (ESCI) identifier

  • 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.