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

Lhoussain El Fadil; Omar Kchit; Hanan Choulli

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

Number Theory 2021-11-12 v1

Authors: Lhoussain El Fadil , Omar Kchit , Hanan Choulli

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.

Keywords

pure number field power integral basis monogeneity polynomial x^60-m square free integer

Cite

@article{arxiv.2111.05899,
  title  = {On power integral bases of certain pure number fields defined by $X^{60}-m$},
  author = {Lhoussain El Fadil and Omar Kchit and Hanan Choulli},
  journal= {arXiv preprint arXiv:2111.05899},
  year   = {2021}
}

Comments

Submitted. arXiv admin note: substantial text overlap with arXiv:2106.01252, arXiv:2106.00004

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

Abstract

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