Non-monogenity in a family of octic fields.

@inproceedings{Gaal2017NonmonogenityIA,
title={Non-monogenity in a family of octic fields.},
author={Istv'an Ga'al and L'aszl'o Remete},
year={2017}
}
Let $m$ be a square-free positive integer, $m\equiv 2,3 \; (\bmod \; 4)$. We show that the number field $K=Q(i,\sqrt[4]{m})$ is non-monogene, that is it does not admit any power integral bases of type $\{1,\alpha,\ldots,\alpha^7\}$. In this infinite parametric family of Galois octic fields we construct an integral basis and show non-monogenity using only congruence considerations. Our method yields a new approach to consider monogenity or to prove non-monogenity in algebraic number fields. It… CONTINUE READING
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