UNJ-Rings

Kosan M. T., Truong Cong Quynh T. C. Q., Zemlicka J.

JOURNAL OF ALGEBRA AND ITS APPLICATIONS, cilt.19, sa.9, 2020 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 19 Sayı: 9
  • Basım Tarihi: 2020
  • Doi Numarası: 10.1142/s0219498820501704
  • 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: UU-ring, UJ-ring, UNJ-ring, unit, Jacobson radical, (semi) regular ring, clean ring, group ring, MODULES
  • Gazi Üniversitesi Adresli: Evet

Özet

In analogy to the elementwise definitions of UU- and UJ-rings, a ring R is called UNJ if 1 + N(R) + J(R) = U(R). After presenting several characterizations and properties, we consider the UNJ-rings within many well-studied classes of rings. In particular, we examine Dedekind finite rings, 2-primal rings, (semi)regular rings, pi-regular rings and rings that satisfy the identity x(2) = x. Finally, we conclude this paper with group UNJ-rings.