On torsion free and cotorsion discrete modules

Abstract

We prove that, if $\mathcal F $ is the class of torsion free discrete modules over a profinite group $G$, that is, the class of discrete $G$-modules which are torsion free as abelian groups, then $({\mathcal F},{\mathcal F}^\bot )$ is a complete cotorsion pair. Moreover, we find a structure theorem for torsion free and cotorsion discrete $G$-modules and for finitely generated cotorsion discrete $G$-modules.