The endomorphism ring of an Artinian module whose homogeneous length is finite

Abstract

Smalø[2] showed that the index of nilpotency of the endomorphism ring of a module M R {M_R} of finite length is bounded by the number max { n A | A R simple } \max \left \{ {{n_A}|{A_R}\;{\text {simple}}} \right \} , where n A {n_A} denotes the number of times A R {A_R} occurs as a factor in a composition chain of M R {M_R} . We give another proof of Smalø’s theorem which leads to an analogous result for artinian modules whose homogeneous length is finite.