Study of a division-like property
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866917677215252480 |
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| author | Khanfir, Robin Seguin, Béranger |
| author_facet | Khanfir, Robin Seguin, Béranger |
| contents | We introduce a weak division-like property for noncommutative rings: a nontrivial ring is fadelian if for all nonzero $a,x$ there exist $b,c$ such that $x=ab+ca$. We prove properties of fadelian rings, and construct examples of such rings which are not division rings, as well as non-Noetherian and non-Ore examples. We have also formalized some of these results in the Lean proof assistant. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_13078 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Study of a division-like property Khanfir, Robin Seguin, Béranger Rings and Algebras 16U20, 13N10, 12E15, 16P40 We introduce a weak division-like property for noncommutative rings: a nontrivial ring is fadelian if for all nonzero $a,x$ there exist $b,c$ such that $x=ab+ca$. We prove properties of fadelian rings, and construct examples of such rings which are not division rings, as well as non-Noetherian and non-Ore examples. We have also formalized some of these results in the Lean proof assistant. |
| title | Study of a division-like property |
| topic | Rings and Algebras 16U20, 13N10, 12E15, 16P40 |
| url | https://arxiv.org/abs/2210.13078 |