On the endomorphism ring of a module noetherian with respect to a torsion theory

IfM is a module torsionfree and noetherian with respect to a torsion theory, ifS is the endomorphism ring ofM, and ifL(S) is the ideal ofS consisting of all endomorphisms with large kernels, thenL(S) is nilpotent and a bound on the index of nilpotency ofL(S) is given.