A note on right-nil and strong-nil skew braces
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| author | Ballester-Bolinches, Adolfo Ferrara, Maria Pérez-Calabuig, Vicent Trombetti, Marco |
| author_facet | Ballester-Bolinches, Adolfo Ferrara, Maria Pérez-Calabuig, Vicent Trombetti, Marco |
| contents | The aim of this short note is to completely answer Questions 2.34 and 2.35 of arXiv:1806.01127. In particular, we show that a finite strong-nil skew brace $B$ of abelian type need not be right-nilpotent, but that this is the case if~$B$ is of nilpotent type and $b\ast b=0$ for all $b\in B$ (our examples show that this is the best possible result). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_11123 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A note on right-nil and strong-nil skew braces Ballester-Bolinches, Adolfo Ferrara, Maria Pérez-Calabuig, Vicent Trombetti, Marco Group Theory Rings and Algebras 16T25, 20F18, 16N99 The aim of this short note is to completely answer Questions 2.34 and 2.35 of arXiv:1806.01127. In particular, we show that a finite strong-nil skew brace $B$ of abelian type need not be right-nilpotent, but that this is the case if~$B$ is of nilpotent type and $b\ast b=0$ for all $b\in B$ (our examples show that this is the best possible result). |
| title | A note on right-nil and strong-nil skew braces |
| topic | Group Theory Rings and Algebras 16T25, 20F18, 16N99 |
| url | https://arxiv.org/abs/2310.11123 |