  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 ${\mathbb{F}}_{q}(T)(\Lambda_{P^{n}})
/{\mathbb{F}}_{q}(T)(\Lambda_{P})$.
