A generalization of UJ-rings

Karabacak F., KOŞAN M. T., Truong Cong Quynh T. C. Q., Dinh Duc Tai D. D. T.

JOURNAL OF ALGEBRA AND ITS APPLICATIONS, vol.20, no.12, 2021 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 20 Issue: 12
  • Publication Date: 2021
  • Doi Number: 10.1142/s0219498821502170
  • Journal Name: JOURNAL OF ALGEBRA AND ITS APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Keywords: Unit, Jacobson radical, UJ-ring, (J)-clean ring, (semi)regular ring, group ring, EXTENSIONS
  • Gazi University Affiliated: Yes

Abstract

The aim of the paper is to characterize the equation 1 + Delta(R) = U(R), where J(R) subset of Delta(R) = {x is an element of R:x + u is an element of U(R) for all u is an element of U(R)} that is the largest Jacobson radical subring of R and U(R) is the set of invertible elements of a ring R. We show that this equation is closely related to U J-rings and rings whose elements can be written as the sum of an idempotent and an element from Delta(R). After presenting several characterizations and properties of this equation, we consider the rings satisfying the equation 1 + Delta(R) = U(R) within many well-studied classes of rings. Finally, we close the paper with group rings.