关于由x^{84}-m定义的纯数域的幂积分基

Pub Date : 2023-06-28 DOI:10.33044/revuma.2836

Lhoussain El Fadil, Omar Kchit, Hanan Choulli

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引用次数: 0

摘要

设$K$为由一元不可约多项式$F(x)=x^{60}-m\in \mathbb{Z}[x]$的复根生成的纯数域，其中$m\neq \pm1$为自由平方整数。本文研究了$K$的单性性。我们证明了如果$m\not\equiv 1\md{4}$, $m\not\equiv \mp 1 \md{9} $和$\overline{m}\not\in\{\mp 1,\mp 7\} \md{25}$，那么$K$是单基因的。但是如果$m\equiv 1\md{4}$, $m\equiv \mp1 \md{9}$或$m\equiv \mp 1\md{25}$，那么$K$就不是单基因的。用实例说明了我们的结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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On power integral bases of certain pure number fields defined by $x^{84}-m$

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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