In 1995, Poonen proved an analogue for Drinfeld modules of the Mordell-Weil theorem. In this talk, we shall generalize his results to the case of -modules. Specifically, let be a -module defined over a finite extension of the fraction field of . Assume that there is an integer such that

with and the matrix is invertible. Then the -module is the direct sum of its torsion submodule, which is finite, with a free -module of rank . Moreover, we also show that the -th tensor power of the Carlitz module is a direct sum of of a free -module of rank and a finite torsion module.