A note on semiprime skew left braces and related semidirect products
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916573860593664 |
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| author | Castelli, Marco |
| author_facet | Castelli, Marco |
| contents | In this paper, we focus on semiprime skew left braces provided by semidirect products. We show that if a semidirect product $B_1\rtimes B_2$ is semiprime and $B_1$ is Artinian, then $B_1$ must be semiprime. Moreover, we prove that the semidirect product of strongly semiprime skew left braces is strongly semiprime. Finally, following \cite[Question $1$]{smoktunowicz2024more}, we provide examples of skew left braces of abelian type that are non-simple and strongly prime. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_20524 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A note on semiprime skew left braces and related semidirect products Castelli, Marco Quantum Algebra In this paper, we focus on semiprime skew left braces provided by semidirect products. We show that if a semidirect product $B_1\rtimes B_2$ is semiprime and $B_1$ is Artinian, then $B_1$ must be semiprime. Moreover, we prove that the semidirect product of strongly semiprime skew left braces is strongly semiprime. Finally, following \cite[Question $1$]{smoktunowicz2024more}, we provide examples of skew left braces of abelian type that are non-simple and strongly prime. |
| title | A note on semiprime skew left braces and related semidirect products |
| topic | Quantum Algebra |
| url | https://arxiv.org/abs/2410.20524 |