Rings whose Non-Invertible Elements are Strongly Nil-Clean
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914757110398976 |
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| author | Danchev, Peter Hasanzadeh, Omid Javan, Arash Moussavi, Ahmad |
| author_facet | Danchev, Peter Hasanzadeh, Omid Javan, Arash Moussavi, Ahmad |
| contents | We consider in-depth and characterize in certain aspects those rings whose non-units are strongly nil-clean in the sense that they are a sum of commuting nilpotent and idempotent. In addition, we examine those rings in which the non-units are uniquely nil-clean in the sense that they are a sum of a nilpotent and an unique idempotent. In fact, we succeeded to prove that these two classes of rings can completely be characterized in terms of already well-studied and fully described sorts of rings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_10651 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Rings whose Non-Invertible Elements are Strongly Nil-Clean Danchev, Peter Hasanzadeh, Omid Javan, Arash Moussavi, Ahmad Rings and Algebras Representation Theory 16S34, 16U60 We consider in-depth and characterize in certain aspects those rings whose non-units are strongly nil-clean in the sense that they are a sum of commuting nilpotent and idempotent. In addition, we examine those rings in which the non-units are uniquely nil-clean in the sense that they are a sum of a nilpotent and an unique idempotent. In fact, we succeeded to prove that these two classes of rings can completely be characterized in terms of already well-studied and fully described sorts of rings. |
| title | Rings whose Non-Invertible Elements are Strongly Nil-Clean |
| topic | Rings and Algebras Representation Theory 16S34, 16U60 |
| url | https://arxiv.org/abs/2404.10651 |