The Monogeneity of Kummer Extensions and Radical Extensions

Hanson Smith

We give necessary and sufficient conditions for the Kummer extension $K:=\mathbb{Q}\left({\zeta }_n,\sqrt[n]{\alpha }\right)$ to be monogenic over $\mathbb{Q}({\zeta }_n)$ with $\sqrt[n]{\alpha }$ as a generato…