Correspondence theorems for nondegenerate modules and their endomorphism rings

Abstract

Let R U _RU be a left R-module whose Morita context is nondegenerate and S = End ( U ) S = {\text {End}}(U) . We show the following: (1) There is a projectivity (that is, an order-preserving bijection) between the complement submodules of R U _RU and the complement left ideals of S; (2) S is a left CS ring if and only if R U _RU is a CS module; (3) S is a Baer and left CS ring if and only if R U _RU is a nonsingular and CS module. Special cases include some earlier works.