Let $K=\mathbb{Q}(\theta)$ be a cubic number filed and $P(X)=X^3-aX-b$ ($a,b$ in $\ZZ$), the monic irreducible polynomial of $\theta$. In this paper we give a sufficient conditions on $a$,$b$ which ensure that $\theta$ is a power basis generator, also we give conditions on relative quadratic extension to be monogenic. As a consequence of this theoretical result we can reach an integral basis of some sextic fields which Neither algebraically split nor arithmetically split.
@article{40042,
title = {On sextic integral bases using relative quadratic extention},
journal = {Boletim da Sociedade Paranaense de Matem\'atica},
volume = {38},
year = {2019},
doi = {10.5269/bspm.v38i4.40042},
language = {EN},
url = {http://dml.mathdoc.fr/item/40042}
}
Sahmoudi, Mohammed; Abderazak, Soullami. On sextic integral bases using relative quadratic extention. Boletim da Sociedade Paranaense de Matemática, Tome 38 (2019) . doi : 10.5269/bspm.v38i4.40042. http://gdmltest.u-ga.fr/item/40042/