Engel's Theorem for Alternative Superalgebras
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913063446249472 |
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| author | Hernández, Isabel da Rocha, Laiz Valim Rodrigues, Rodrigo Lucas |
| author_facet | Hernández, Isabel da Rocha, Laiz Valim Rodrigues, Rodrigo Lucas |
| contents | In this paper, a nilpotency criterion is given for finite dimensional alternative superalgebras in the spirit of Engel's Theorem for Jordan superalgebras over infinite fields provided by Shestakov and Okunev. For alternative superalgebras, no restrictions on the cardinality of the ground field are required. Furthermore, we establish some connections between the concepts of graded-nil and nilpotent alternative superalgebras, and we also exhibit an example of an Engelian commutative power-associative superalgebra of dimension $4$ which is not nilpotent. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_18073 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Engel's Theorem for Alternative Superalgebras Hernández, Isabel da Rocha, Laiz Valim Rodrigues, Rodrigo Lucas Rings and Algebras In this paper, a nilpotency criterion is given for finite dimensional alternative superalgebras in the spirit of Engel's Theorem for Jordan superalgebras over infinite fields provided by Shestakov and Okunev. For alternative superalgebras, no restrictions on the cardinality of the ground field are required. Furthermore, we establish some connections between the concepts of graded-nil and nilpotent alternative superalgebras, and we also exhibit an example of an Engelian commutative power-associative superalgebra of dimension $4$ which is not nilpotent. |
| title | Engel's Theorem for Alternative Superalgebras |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2501.18073 |