Joubert's theorem fails in characteristic 2
Number Theory
2017-02-22 v2
Abstract
Let L/K be a separable field extension of degree 6. An 1867 theorem of P. Joubert asserts that if char(K) is different from 2 then L is generated over K by an element whose minimal polynomial is of the form t^6 + a t^4 + b t^2 + ct + d for some a, b, c, d in K. We show that this theorem fails in characteristic 2.
Cite
@article{arxiv.1406.7529,
title = {Joubert's theorem fails in characteristic 2},
author = {Zinovy Reichstein},
journal= {arXiv preprint arXiv:1406.7529},
year = {2017}
}
Comments
5 pages, new material added