Rings Whose Non-Invertible Elements Are Nil-Clean
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911878523912192 |
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| author | Danchev, Peter Javan, Arash Hasanzadeh, Omid Moussavi, Ahmad |
| author_facet | Danchev, Peter Javan, Arash Hasanzadeh, Omid Moussavi, Ahmad |
| contents | We systematically study those rings whose non-units are a sum of an idempotent and a nilpotent. Some crucial characteristic properties are completely described as well as some structural results for this class of rings are obtained. This work somewhat continues two publications on the subject due to Diesl (J. Algebra, 2013) and Karimi-Mansoub et al. (Contemp. Math., 2018). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_09961 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Rings Whose Non-Invertible Elements Are Nil-Clean Danchev, Peter Javan, Arash Hasanzadeh, Omid Moussavi, Ahmad Rings and Algebras Representation Theory 16S34, 16U60 We systematically study those rings whose non-units are a sum of an idempotent and a nilpotent. Some crucial characteristic properties are completely described as well as some structural results for this class of rings are obtained. This work somewhat continues two publications on the subject due to Diesl (J. Algebra, 2013) and Karimi-Mansoub et al. (Contemp. Math., 2018). |
| title | Rings Whose Non-Invertible Elements Are Nil-Clean |
| topic | Rings and Algebras Representation Theory 16S34, 16U60 |
| url | https://arxiv.org/abs/2405.09961 |