# 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} }

- Published 2017
DOI:10.1216/RMJ-2017-47-3-817

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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## Non-monogeneity in a family of sextic fields

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