Radical Extensions for the Carlitz--Hayes Module

Let $L\mathrm{/}K$ be a finite extension of congruence function fields. We say that $L\mathrm{/}K$ is a {\it radical extension} if $L$ is generated by roots of polynomials $u^M-\alpha \in K[u]$, where $u^M$ is the action of Carlitz-Hayes. We study a special class of these extensions, the {\it radical cyclotomic} extensions. We prove that any radical cyclotomic extension has order a power of the characteristic of $K$. We also give bounds for the Carlitz-Hayes torsion of these extensions.