Two results on modules whose endomorphism ring is semilocal

The aim of this paper is twofold. On the one hand, we show that the dual Goldie dimension codim(End(MR)) of the endomorphism ring End(M R) of a module MR can be used as a measure of the dimension of the module MR. On the other hand, we prove under suitable hypotheses the validity of the Krull-Schmidt Theorem for infinite direct sums of modules with homogeneous semilocal endomorphism rings. © 2004 Kluwer Academic Publishers.