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arXiv · 2401.03449

Rings Whose Clean Elements Are Uniquely Strongly Clean

Peter Danchev·Omid Hasanzadeh·Ahmad Moussavi
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Abstract

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.

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Peter Danchev, Omid Hasanzadeh, Ahmad Moussavi. 2024-01-07. Rings Whose Clean Elements Are Uniquely Strongly Clean. https://arxiv.org/abs/2401.03449

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