On power integral bases for certain pure number fields defined by x24 – m

@article{Fadil2020OnPI,
  title={On power integral bases for certain pure number fields defined by x24 – m},
  author={Lhoussain El Fadil},
  journal={arXiv: Number Theory},
  year={2020}
}
  • L. E. Fadil
  • Published 19 June 2020
  • Mathematics
  • arXiv: Number Theory
Let $K=\mathbb{Q}(\alpha)$ be a number field generated by a complex root $\alpha$ of a monic irreducible polynomial $f(x)=x^{12}-m$, with $m\neq 1$ is a square free rational integer. In this paper, we prove that if $m \equiv 2$ or $3$ (mod 4) and $m\not\equiv \mp 1$ (mod 9), then the number field $K$ is monogenic. If $m \equiv 1$ (mod 8) or $m\equiv \mp 1$ (mod 9), then the number field $K$ is not monogenic. 
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