Rings Whose Clean Elements Are Uniquely Strongly Clean
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866913188358914048 |
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| author | Danchev, Peter Hasanzadeh, Omid Moussavi, Ahmad |
| author_facet | Danchev, Peter Hasanzadeh, Omid Moussavi, Ahmad |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_03449 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Rings Whose Clean Elements Are Uniquely Strongly Clean Danchev, Peter Hasanzadeh, Omid Moussavi, Ahmad Rings and Algebras Representation Theory 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. |
| title | Rings Whose Clean Elements Are Uniquely Strongly Clean |
| topic | Rings and Algebras Representation Theory |
| url | https://arxiv.org/abs/2401.03449 |