On the Goldie Dimension of Hereditary Rings and Modules

Details On the Goldie Dimension of Hereditary Rings and Modules On the Goldie Dimension of Hereditary Rings and Modules

2005-12-14

arxiv.org/abs/math/0512337v1

Mathematics

Rings and Algebras

13 pages

Scientific paper

We find a bound for the Goldie dimension of hereditary modules in terms of the cardinality of the generator sets of its quasi-injective hull. Several consequences are deduced. In particular, it is shown that every right hereditary module with countably generated quasi-injective hull is noetherian. Or that every right hereditary ring with finitely generated injective hull is artinian, thus answering a long standing open question posed by Dung, Gomez Pardo and Wisbauer.

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