On rings determined by their idempotents and units

Çetin M., KOŞAN M. A., Žemlička J.

Communications in Algebra, cilt.51, sa.7, ss.2820-2829, 2023 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 51 Sayı: 7
  • Basım Tarihi: 2023
  • Doi Numarası: 10.1080/00927872.2023.2173762
  • Dergi Adı: Communications in Algebra
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Sayfa Sayıları: ss.2820-2829
  • Anahtar Kelimeler: (Abelian) regular ring, clean ring, semiperfect ring, semicommutative ring, symmetric ring
  • Gazi Üniversitesi Adresli: Evet

Özet

© 2023 Taylor & Francis Group, LLC.This paper describes properties of three certain classes of rings determined by conditions on idempotents and units, namely, the condition that any two generators of each principal right ideal are associated (UG rings), the condition that every principal right ideal is generated by a sum of a unit and an idempotent (Pr), and the condition xy = 0 implies xsy = 0 for a sum of idempotent and unit s and any elements x, y of a ring (idun-semicommutative rings). It is proved that the class of all UG rings contains every local as well as every von Neumann regular ring, and the condition Pr is satisfied by both semiperfect and regular rings. Both local and abelian regular rings are proved to be necessarily idun-semicommutative. For all three classes are presented some closure properties and illustrating examples.