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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| Accès en ligne: | https://arxiv.org/abs/2503.06600 |
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| _version_ | 1866913727233654784 |
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| author | Cohen, Stephen D. Danchev, Peter V. Silva, Tomás Oliveira e |
| author_facet | Cohen, Stephen D. Danchev, Peter V. Silva, Tomás Oliveira e |
| contents | We classify those finite fields $\mathbb{F}_q$, for $q$ a power of some fixed prime number, whose members are the sum of an $n$-potent element with $n>1$ and a 4-potent element. It is shown that there are precisely ten non-trivial pairs $(q,n)$ for which this is the case.
This continues a recent publication by Cohen-Danchev et al. in Turk. J. Math. (2024) in which the tripotent version was examined in-depth as well as it extends recent results of this branch established by Abyzov-Tapkin in Sib. Math. J. (2024). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_06600 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Finite fields whose members are the sum of a potent and a 4-potent Cohen, Stephen D. Danchev, Peter V. Silva, Tomás Oliveira e Rings and Algebras Commutative Algebra Number Theory 16D60, 16U60, 11T30 We classify those finite fields $\mathbb{F}_q$, for $q$ a power of some fixed prime number, whose members are the sum of an $n$-potent element with $n>1$ and a 4-potent element. It is shown that there are precisely ten non-trivial pairs $(q,n)$ for which this is the case. This continues a recent publication by Cohen-Danchev et al. in Turk. J. Math. (2024) in which the tripotent version was examined in-depth as well as it extends recent results of this branch established by Abyzov-Tapkin in Sib. Math. J. (2024). |
| title | Finite fields whose members are the sum of a potent and a 4-potent |
| topic | Rings and Algebras Commutative Algebra Number Theory 16D60, 16U60, 11T30 |
| url | https://arxiv.org/abs/2503.06600 |