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.
|Journal||Algebras and Representation Theory|
|Publication status||Published - 1 Dec 2004|
- Endomorphism ring
- Krull-Schmidt theorem
- Semilocal ring