Unit Uniquely Clean Rings
Abstract
We define the class of {\it unit uniquely clean} rings ({\it UnitUC} for short), that is a common generalization of uniquely clean rings and strongly nil clean rings. Abelian {\it UnitUC} rings are uniquely clean and {\it UnitUC} rings with nil Jacobson radical are strongly nil clean. These rings also generalize the UUC and CUC rings, defined by Calugareanu-Zhou in Mediterranean J. Math. (2023), which are rings whose clean elements are uniquely clean. These rings are also represent a natural generalization of the Boolian rings in that a ring is {\it UnitUC} if, and only if, it is exchange and Boolean modulo the Jacobson radical. The behavior of {\it UnitUC} rings under group ring and matrix ring extensions is investigated. Several examples are provided to explain and delimit the results.
Keywords
Cite
@article{arxiv.2509.17573,
title = {Unit Uniquely Clean Rings},
author = {Mina Doostalizadeh and Ahmad Moussavi and Peter Danchev},
journal= {arXiv preprint arXiv:2509.17573},
year = {2025}
}
Comments
15 pages