NONSINGULAR RETRACTABLE MODULES AND THEIR ENDOMORPHISM-RINGS

A module R(M) is said to be retractable if Hom(R) (M, U) not-equal 0 for each nonzero submodule U of M. M is said to be a CS module if every complement submodule of M is a direct summand in M. Retractable modules are compared to nondegenerate modules on the one hand and to e-retractable modules on the other (nondegenerate implies retractable implies e-retractable); and it is shown that if M is nonsingular and retractable, then End(R) M is a left CS ring if only if M is a CS module.