Calculating power integral bases in some quartic fields corresponding to monogenic families of polynomials
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866912027927117824 |
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| author | Gaál, István |
| author_facet | Gaál, István |
| contents | J. Harrington and L. Jones characterized monogenity of four new parametric families of quartic polynomials with various Galois groups. A short time later P. Voutier added a cyclic family. In this note we intend to describe all generators of power integral bases in the number fields generated by a root of the monogenic polynomials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_13429 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Calculating power integral bases in some quartic fields corresponding to monogenic families of polynomials Gaál, István Number Theory 11Y50, 11R04, 11D25 J. Harrington and L. Jones characterized monogenity of four new parametric families of quartic polynomials with various Galois groups. A short time later P. Voutier added a cyclic family. In this note we intend to describe all generators of power integral bases in the number fields generated by a root of the monogenic polynomials. |
| title | Calculating power integral bases in some quartic fields corresponding to monogenic families of polynomials |
| topic | Number Theory 11Y50, 11R04, 11D25 |
| url | https://arxiv.org/abs/2405.13429 |