On monogenity of certain pure number fields defined by $x^{p^r}-m$

Hamid Ben Yakkou; Lhoussain El Fadil

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arXiv · 2102.01967

On monogenity of certain pure number fields defined by $x^{p^r}-m$

Hamid Ben Yakkou·Lhoussain El Fadil

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Abstract

Let $K = \mathbb{Q} (\alpha) $ be a pure number field generated by a complex root $\alpha$ a monic irreducible polynomial $ F(x) = x^{p^r} -m$, with $ m \neq 1 $ is a square free rational integer, $p$ is a rational prime integer, and $r$ is a positive integer. In this paper, we study the monogenity of $K$. We prove that if {{$\nu_p(m^p-m)=1$}}, then $K$ is monogenic. But if $r\ge p$ and {$\nu_p(m^{p}-m)> p$}, then $K$ is not monogenic. Some illustrating examples are given.

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BibTeX RIS

Hamid Ben Yakkou, Lhoussain El Fadil. 2021-02-03. On monogenity of certain pure number fields defined by $x^{p^r}-m$. https://arxiv.org/abs/2102.01967

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