A semifield of order 128 and fractional dimension $\frac{7}{3}$ relative to one of its subsemifields
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866909563990573056 |
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| author | Rúa, Ignacio Fernández Álvarez, Elías Fernández-Combarro |
| author_facet | Rúa, Ignacio Fernández Álvarez, Elías Fernández-Combarro |
| contents | In this short note, an example of a semifield of order 128 containing the Galois field $\mathbb{F}_8$ is given. Up to our knowledge, this is the first example supporting the following problem by Cordero and Chen (2013): ``There exist semifield planes of order $2^t$, for any integers $t$ relatively prime to 3 that admit semifield subplanes of order $2^3$''. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_03033 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A semifield of order 128 and fractional dimension $\frac{7}{3}$ relative to one of its subsemifields Rúa, Ignacio Fernández Álvarez, Elías Fernández-Combarro General Mathematics In this short note, an example of a semifield of order 128 containing the Galois field $\mathbb{F}_8$ is given. Up to our knowledge, this is the first example supporting the following problem by Cordero and Chen (2013): ``There exist semifield planes of order $2^t$, for any integers $t$ relatively prime to 3 that admit semifield subplanes of order $2^3$''. |
| title | A semifield of order 128 and fractional dimension $\frac{7}{3}$ relative to one of its subsemifields |
| topic | General Mathematics |
| url | https://arxiv.org/abs/2504.03033 |