International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 68, Pages 4263-4323

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

Received 5 March 2002

Copyright © 2003 Max-Albert Knus and Jean-Pierre Tignol. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.