Several authors have considered the infinite parametric family of simplest quartic fields $K_t=\mathbb Q(\xi)$. In this paper, we explicitly give all generators of power integral bases in the ring of integers $\mathbb Z_K$ of$K_t$ assuming that $t^2+16$is not divisible by an odd square. We use a well known general algorithm for calculating power integral bases in quartic fields.
Publié le : 2005-05-14
Classification:
Power integral bases,
simplest quartic fields,
index form equations,
11D57,
11Y50
@article{1128100125,
author = {Olajos, P\'eter},
title = {Power integral bases in the family of simplest quartic fields},
journal = {Experiment. Math.},
volume = {14},
number = {1},
year = {2005},
pages = { 129-132},
language = {en},
url = {http://dml.mathdoc.fr/item/1128100125}
}
Olajos, Péter. Power integral bases in the family of simplest quartic fields. Experiment. Math., Tome 14 (2005) no. 1, pp. 129-132. http://gdmltest.u-ga.fr/item/1128100125/