  In this article we provide a complete characterization of abelian group rings
which are K\"{o}the rings. We also provide characterizations of (possibly
non-abelian) group rings over division rings which are K\"{o}the rings, both in
characteristic zero and in prime characteristic, and prove a Maschke type
result for pure semisimplicity of group rings. Furthermore, we illustrate our
results by several examples.
