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On the Goldie Dimension of Hereditary Rings and Modules

H. Q. Dinh·P. A. Guil Asensio·S. R. Lopez-Permouth
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Abstract

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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H. Q. Dinh, P. A. Guil Asensio, S. R. Lopez-Permouth. 2005-12-14. On the Goldie Dimension of Hereditary Rings and Modules. https://arxiv.org/abs/math/0512337

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