Nonsingular Semiperfect CS-Rings

In this paper the structure of right nonsingular semiperfect right CS-rings has been considered. Under certain conditions these rings are shown to be direct sums of triangular blocked matrix rings over Ore domains. As a by-product it follows that then × nmatrix ring over a local domainD,n > 1, is a right CS-ring if and only ifDis a right and left valuation domain.