Rings in which every unit is a sum of a nilpotent and an idempotent - Karimi-Mansoub, Arezou; Kosan, Tamer; Zhou, Yiqiang (Amer Mathematical Soc, 2018)
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.
Keywords: unit; idempotent; nilpotent; nil-clean ring; strongly nil-clean ring; clean ring; semipotent ring; UU ring; UNC ring; group ring