  As a generalization of Drinfeld modules, Greg Anderson introduced abelian
t-modules and t-motives over a perfect field. In this article we study relative
versions of these over rings. We investigate isogenies among them. Our main
results state that every isogeny possesses a dual isogeny in the opposite
direction, and that a morphism between abelian t-modules is an isogeny if and
only if the corresponding morphism between their associated t-motives is an
isogeny. We also study torsion submodules of abelian t-modules which in general
are non-reduced group schemes. They can be obtained from the associated
t-motive via the finite shtuka correspondence of Drinfeld and Abrashkin. The
inductive limits of torsion submodules are the function field analogs of
p-divisible groups. These limits correspond to the local shtukas attached to
the t-motives associated with the abelian t-modules. In this sense the theory
of abelian t-modules is captured by the theory of t-motives.
