Lhoussain El Fadil, Omar Kchit, Hanan Choulli
Published 2021-11-10Version 1
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.
Comments: Submitted. arXiv admin note: substantial text overlap with arXiv:2106.01252, arXiv:2106.00004
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On monogenity of certain pure number fields of degrees $2^r\cdot3^k\cdot7^s$
On monogenity of certain pure number fields defined by $x^{p^r}-m$
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