Rings in which every unit is a sum of a nilpotent and an idempotent

Karimi-Mansoub A., Kosan T., Zhou Y.

ADVANCES IN RINGS AND MODULES, cilt.715, ss.189-203, 2018 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 715
  • Basım Tarihi: 2018
  • Doi Numarası: 10.1090/conm/715/14412
  • Dergi Adı: ADVANCES IN RINGS AND MODULES
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), MathSciNet, zbMATH
  • Sayfa Sayıları: ss.189-203
  • Anahtar Kelimeler: unit, idempotent, nilpotent, nil-clean ring, strongly nil-clean ring, clean ring, semipotent ring, UU ring, UNC ring, group ring, ELEMENT
  • Gazi Üniversitesi Adresli: Hayır

Özet

A ring R is a UU ring if every unit is unipotent, or equivalently if every unit is a sum of a nilpotent and an idempotent that commute. These rings have been investigated in Calugareanu [3] and in Danchev and Lam [7]. In this paper, two generalizations of UU rings are discussed. We study rings for which every unit is a sum of a nilpotent and an idempotent, and rings for which every unit is a sum of a nilpotent and two idempotents that commute with one another.