English

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

R2 v1 2026-06-22T04:50:30.615Z