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, cilt.20, sa.12, 2021 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 20 Sayı: 12
  • Basım Tarihi: 2021
  • Doi Numarası: 10.1142/s0219498821502170
  • Dergi Adı: JOURNAL OF ALGEBRA AND ITS APPLICATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Anahtar Kelimeler: Unit, Jacobson radical, UJ-ring, (J)-clean ring, (semi)regular ring, group ring, EXTENSIONS
  • Gazi Üniversitesi Adresli: Evet

Özet

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.