The notion of a simple ring DGderived from a group ring KG is introduced in case K is a field and G is an infinite residually finite group. The close link between DGand KGis exploited in both directions: first, for a simple proof of the Kaplansky's conjecture concerning direct finiteness of KG. Second, to show that DGprovides counter-examples to some conjectures dealing with von Neumann regular rings and the rings all of whose one-sided ideals are generated by idempotents.