2024/01/07 by Peter Danchev, Omid Hasanzadeh, Danchev, Peter +3
Computer Science · Mathematics · #Advanced Algebra and Logic #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA) #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2401.03449
openalex publication_date 2024/01/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We define the class of \it CUSC rings, that are those rings whose clean elements are uniquely strongly clean. These rings are a common generalization of the so-called \it USC rings, introduced by Chen-Wang-Zhou in J. Pure & Applied Algebra (2009), which are rings whose elements are uniquely strongly clean. These rings also generalize the so-called \it CUC rings, defined by Calugareanu-Zhou in Mediterranean J. Math. (2023), which are rings whose clean elements are uniquely clean. We establish that a ring is USC if, and only if, it is simultaneously CUSC and potent. Some other interesting relationships with CUC rings are obtained as well.