ENDOMORPHISM-RINGS OF NONDEGENERATE MODULES

Let (R)M be a left R-module whose Morita context is nondegenerate, S = End((R)M), and N = Hom((R)M, R). If (R)M is also nonsingular, then th e main results of Khuri (Proc. Amer. Math. Sec. 96 (1986), 553-559) ar e the following: (1) S is left (right) strongly modular if and only if any element of S which has zero kernel in (R)M(N-R) has essential ima ge in (R)M(N-R);(2) S is a left (right) Utumi ring if and only if ever y submodule a U-R of (R)M (U-R Of N-R) such that U perpendicular to = 0 (perpendicular to U = 0) is essential in RM(NR) In this paper, we show that the same results hold in any nondegenerate Morita context wi thout (R)M being nonsingular and that S is right nonsingular if and on ly if N-R is nonsingular.