Rings Whose Non-Invertible Elements are Strongly Weakly Nil-Clean
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866916664033935360 |
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| author | Danchev, Peter Doostalizadeh, Mina Hasanzadeh, Omid Javan, Arash Moussavi, Ahmad |
| author_facet | Danchev, Peter Doostalizadeh, Mina Hasanzadeh, Omid Javan, Arash Moussavi, Ahmad |
| contents | The target of the present work is to give a new insight in the theory of {\it strongly weakly nil-clean} rings, recently defined by Kosan and Zhou in the Front. Math. China (2016) and further explored in detail by Chen-Sheibani in the J. Algebra Appl. (2017). Indeed, we consider those rings whose non-units are strongly weakly nil-clean and succeed to establish that this class of rings is strongly $π$-regular and, even something more, that it possesses a complete characterization in terms of the Jacobson radical and sections of the $2\times 2$ full matrix ring. Additionally, some extensions like Morita context rings and groups rings are also studied in this directory. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_21547 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Rings Whose Non-Invertible Elements are Strongly Weakly Nil-Clean Danchev, Peter Doostalizadeh, Mina Hasanzadeh, Omid Javan, Arash Moussavi, Ahmad Rings and Algebras Representation Theory 16S34, 16U60 The target of the present work is to give a new insight in the theory of {\it strongly weakly nil-clean} rings, recently defined by Kosan and Zhou in the Front. Math. China (2016) and further explored in detail by Chen-Sheibani in the J. Algebra Appl. (2017). Indeed, we consider those rings whose non-units are strongly weakly nil-clean and succeed to establish that this class of rings is strongly $π$-regular and, even something more, that it possesses a complete characterization in terms of the Jacobson radical and sections of the $2\times 2$ full matrix ring. Additionally, some extensions like Morita context rings and groups rings are also studied in this directory. |
| title | Rings Whose Non-Invertible Elements are Strongly Weakly Nil-Clean |
| topic | Rings and Algebras Representation Theory 16S34, 16U60 |
| url | https://arxiv.org/abs/2503.21547 |