Die absteigende Loewy-Länge von Endomorphismenringen

We give an upper bound for the descending Loewy length of the ring S=End(M), where M is a semi-artinian R-module satisfying some extra-conditions.In case M is of finite length, our main result specializes to the following result, which improves a theorem of Smalø (3]): The index of nilpotency of Ra(S) is bounded by the number max{l_A¦A is a simple R-module occuring in the socle of M}, where l_A denotes the number of times the isomorphism type of A occurs as a factor in a composition chain of M.