On the monogenity of quartic number fields defined by $x^4+ax^2+b$
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866914679287185408 |
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| author | Fadil, Lhoussain El Gaál, István |
| author_facet | Fadil, Lhoussain El Gaál, István |
| contents | For any quartic number field $K$ generated by a root $α$ of an irreducible trinomial of type $x^4+ax^2+b\in Z[x]$, we characterize when $Z[α]$ is integrally closed. Also for $p=2,3$, we explicitly give the highest power of $p$ dividing $i(K)$, the common index divisor of $K$. For a wide class of monogenic trinomials of this type we prove that up to equivalence there is only one generator of power integral bases in $K=Q(α)$. We illustrate our statements with a series of examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_03226 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On the monogenity of quartic number fields defined by $x^4+ax^2+b$ Fadil, Lhoussain El Gaál, István Number Theory 11R04, 11Y40, 11R09, 11R21 For any quartic number field $K$ generated by a root $α$ of an irreducible trinomial of type $x^4+ax^2+b\in Z[x]$, we characterize when $Z[α]$ is integrally closed. Also for $p=2,3$, we explicitly give the highest power of $p$ dividing $i(K)$, the common index divisor of $K$. For a wide class of monogenic trinomials of this type we prove that up to equivalence there is only one generator of power integral bases in $K=Q(α)$. We illustrate our statements with a series of examples. |
| title | On the monogenity of quartic number fields defined by $x^4+ax^2+b$ |
| topic | Number Theory 11R04, 11Y40, 11R09, 11R21 |
| url | https://arxiv.org/abs/2204.03226 |