Work

Unit uniquely clean rings

Year: 2026

Type: article

Abstract: In this paper, we define and explore the class of unit uniquely clean rings (or just UnitUC for short), that is a common generalization of the classes of uniquely clean rings and strongly nil-clean rings; in particular, Abelian UnitUC rings are uniquely clean and UnitUC rings with nil Jacobson radical are strongly nil-clean. These rings also generalize the so-called UUC and CUC rings as defined by Călugăreanu–Zhou in Mediterranean J. Math. (2023), which are rings whose clean elements are uniquely clean. These rings also represent a natural expansion of the classical Boolean rings in the sense that a ring is UnitUC if, and only if, it is exchange and Boolean modulo the Jacobson radical. The behavior of UnitUC rings under group ring and matrix ring extensions is investigated as well. In addition, several nontrivial examples are provided to explain and delimit the obtained results.

Source: Asian-European Journal of Mathematics

DOI: 10.1142/s1793557126500415

Authors: Mina Doostalizadeh, Ahmad Moussavi, Peter Danchev

Institutions: Tarbiat Modares University, Bulgarian Academy of Sciences, Institute of Mathematics and Informatics

Language: English

Topic: Rings, Modules, and Algebras

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7140713569

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