Skew braces with no proper left ideals
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866916060219834368 |
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| author | Tsang, Cindy |
| author_facet | Tsang, Cindy |
| contents | A skew brace $A = (A,\cdot,\circ)$ is said to be \textit{left-simple} if $A\neq1$ and it has no left ideal other than $1$ and $A$. The purpose of this paper is to give a partial classification of the finite left-simple skew braces. A result of Stefanello and Trappeniers implies that finite left-simple skew braces correspond precisely to minimal Hopf--Galois structures on finite Galois extensions of fields. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_09320 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Skew braces with no proper left ideals Tsang, Cindy Group Theory Rings and Algebras A skew brace $A = (A,\cdot,\circ)$ is said to be \textit{left-simple} if $A\neq1$ and it has no left ideal other than $1$ and $A$. The purpose of this paper is to give a partial classification of the finite left-simple skew braces. A result of Stefanello and Trappeniers implies that finite left-simple skew braces correspond precisely to minimal Hopf--Galois structures on finite Galois extensions of fields. |
| title | Skew braces with no proper left ideals |
| topic | Group Theory Rings and Algebras |
| url | https://arxiv.org/abs/2602.09320 |