Hilbert's Theorem 90, periodicity, and roots of Artin-Schreier polynomials

S. P. Glasby

Let $E/F$ be a cyclic field extension of degree $n$, and let $\sigma$ generate the group $\mathrm{Gal}(E/F)$. If ${\mathrm{Tr}}_F^E(y)={\sum }_{i=0}^{n-1}{\sigma }^{i}y=0$, then the additive form of Hilber…