Abstract
In this paper, we obtain the structure of the endomorphism rings of nonsingular semiperfect progenerator uniform CS modules with uniform submodule. It is shown that such rings are direct sums of indecomposable right CS rings and a ring with no uniform right ideal. In particular, right nonsingular semiperfect right uniform CS rings with uniform right ideal are direct sums of indecomposable right CS rings and a ring with no uniform right ideal. Also it is shown that a progenerator R- \module is uniform CS if and only if its endomorphism ring is right uniform CS.