Cogalois theory and Drinfeld modules

In this paper we generalize the results of \cite{sanchez} to rank one Drinfeld modules with class number one. We show that, in the present form, there does not exist a cogalois theory for Drinfeld modules of rank or class number larger than one. We also consider the torsion of the Carlitz module for the extension ${$\mathbb{F}$}{q}(T)(\Lambda{P^{n}}) /{$\mathbb{F}$}{q}(T)(\Lambda{P})$.