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arXiv · 2111.05899

On power integral bases of certain pure number fields defined by $X^{60}-m$

Lhoussain El Fadil·Omar Kchit·Hanan Choulli
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Abstract

Let $K$ be a pure number field generated by a complex root of a monic irreducible polynomial $F(x)=x^{60}-m\in \mathbb{Z}[x]$, with $m\neq \pm1$ a square free integer. In this paper, we study the monogeneity of $K$. We prove that if $m\not\equiv 1\md{4}$, $m\not\equiv \mp 1 \md{9} $ and $\overline{m}\not\in\{\mp 1,\mp 7\} \md{25}$, then $K$ is monogenic. But if $m\equiv 1\md{4}$, $m\equiv \mp1 \md{9}$, or $m\equiv \mp 1\md{25}$, then $K$ is not monogenic. Our results are illustrated by examples.

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Lhoussain El Fadil, Omar Kchit, Hanan Choulli. 2021-11-10. On power integral bases of certain pure number fields defined by $X^{60}-m$. https://arxiv.org/abs/2111.05899

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