  In this note, we establish conditions under which the union of an increasing
sequence of completely decomposable modules over domains are again completely
decomposable. In our investigation, the condition of purity of modules is
crucial. In fact, the main result reported in this work states that a module is
completely decomposable when it is the union of a countable, ascending chain of
completely decomposable, pure submodules, providing thus a generalization of
Hill's criterion of freeness from abelian group theory.
