Two Results on Modules whose Endomorphism Ring is Semilocal |
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| Authors: | Alberto Facchini Dolors Herbera |
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| Institution: | (1) Dipartimento di Matematica Pura e Applicata, Università di Padova, 35131 Padova, Italy;(2) Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Barcelona, Spain |
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| Abstract: | The aim of this paper is twofold. On the one hand, we show that the dual Goldie dimension codim(End(M
R
)) of the endomorphism ring End(M
R
) of a module M
R
can be used as a measure of the dimension of the module M
R
. 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. |
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| Keywords: | module endomorphism ring semilocal ring Krull– Schmidt theorem |
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