Radical extensions for the Carlitz module

Abstract

Let L/K be a finite extension of congruence function fields. We say that L/K is a radical extension if L is generated by roots of polynomials CM(u)−α∈K[u], where CM(u) is the action of Carlitz. We study a special class of these extensions, the pure coradical extensions. We prove that any pure coradical extension has order a power of the characteristic of K. We also give bounds for the Carlitz torsion of these extensions.