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.
Two results on modules whose endomorphism ring is semilocal
FACCHINI, ALBERTO;
2004
Abstract
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.
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