International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 68, Pages 4263-4323
doi:10.1155/S0161171203203458
Quartic exercises
Max-Albert Knus1
and Jean-Pierre Tignol2
1Departement Mathematik, ETH Zentrum, Zürich CH-8092, Switzerland
2Institut de Mathématique Pure et Appliquée, Université Catholique de Louvain, Louvain-la-Neuve B-1348, Belgium
Abstract
A correspondence between quartic étale algebras over a field and quadratic étale extensions of cubic étale algebras is set up and investigated. The basic constructions are laid out in general for sets with a profinite group action and for torsors, and translated in terms of étale algebras and Galois algebras. A parametrization of cyclic quartic algebras is given.