Power integral bases in a family of octic fields
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866929684791427072 |
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| author | Gaál, István |
| author_facet | Gaál, István |
| contents | Several recent results prove the monogenity of some polynomials. In these cases the root of the polynomial generates a power integral basis in the number field generated by the root. A straightforward question is whether such a number field admits other generators of power integral bases? We have investigated this problem in some previous papers and here we extend this research to a family of octic polynomials, following a recent result of L. Jones. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_13519 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Power integral bases in a family of octic fields Gaál, István Number Theory 11Y50, 11R04, 11D25 Several recent results prove the monogenity of some polynomials. In these cases the root of the polynomial generates a power integral basis in the number field generated by the root. A straightforward question is whether such a number field admits other generators of power integral bases? We have investigated this problem in some previous papers and here we extend this research to a family of octic polynomials, following a recent result of L. Jones. |
| title | Power integral bases in a family of octic fields |
| topic | Number Theory 11Y50, 11R04, 11D25 |
| url | https://arxiv.org/abs/2501.13519 |