Reversibility of Rings with Respect to the Jacobson Radical

Calci M. B., Chen H., HALICIOĞLU S., Harmanci A.

MEDITERRANEAN JOURNAL OF MATHEMATICS, vol.14, no.3, 2017 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 14 Issue: 3
  • Publication Date: 2017
  • Doi Number: 10.1007/s00009-017-0938-2
  • Journal Name: MEDITERRANEAN JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Keywords: Reversible ring, J-reversible ring, central reversible ring, weakly reversible ring, ring extension, EXCHANGE RINGS
  • Ankara 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-reversible if for any a, b is an element of R, ab = 0 implies ba is an element of J(R). In this paper, we give some properties of J-reversible rings. We prove that some results of reversible rings can be extended to J-reversible rings for this general setting. We show that J-quasipolar rings, local rings, semicommutative rings, central reversible rings and weakly reversible rings are J-reversible. As an application it is shown that every J-clean ring is directly finite.