Submission: 2015, Sep 10
Motivated by the classical theorems of Ch. Hermite and P. Joubert, we give a necessary and sufficient condition for an integer n, a field F_0 and a prime p to have the following property: for every etale algebra E/F of degree n, where F is a p-field containing F_0, there exists an element a in E such that F[a] = E and tr(a) = tr(a^p) = 0.
2010 Mathematics Subject Classification: 12F10, 14J70, 14G05
Keywords and Phrases: Hermite-Joubert problem, étale algebra, hypersurface, rational point, p-field
Full text: dvi.gz 46 k, dvi 107 k, ps.gz 999 k, pdf.gz 223 k, pdf 250 k.