  In this work, we investigate conditions under which unions of ascending
chains of modules which are isomorphic to direct sums of ideals of an integral
domain are again isomorphic to direct sums of ideals. We obtain generalizations
of the Pontryagin-Hill theorems for modules which are direct sums of ideals of
h-local Pr\"{u}fer domains. Particularly, we prove that a torsion-free module
over a Dedekind domain with a countable number of maximal ideals is isomorphic
to a direct sum of ideals if it is the union of a countable ascending chain of
pure submodules which are isomorphic to direct sums of ideals.
