On the monogenity of quartic number fields defined by $x^4+ax^2+b$

Lhoussain El Fadil; István Gaál

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arXiv · 2204.03226

On the monogenity of quartic number fields defined by $x^4+ax^2+b$

Lhoussain El Fadil·István Gaál

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Abstract

For any quartic number field $K$ generated by a root $\alpha$ of an irreducible trinomial of type $x^4+ax^2+b\in Z[x]$, we characterize when $Z[\alpha]$ 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 $K=Q(\alpha)$. We illustrate our statements with a series of examples.

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Lhoussain El Fadil, István Gaál. 2022-04-07. On the monogenity of quartic number fields defined by $x^4+ax^2+b$. https://arxiv.org/abs/2204.03226

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