CORRESPONDENCE THEOREMS FOR NONDEGENERATE MODULES AND THEIR ENDOMORPHISM-RINGS

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