On the Goldie Dimension of Hereditary Rings and Modules

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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.
13 pages

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Rings and Algebras, 16D50; 16D90; 16L30

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http://salesiana.dossiersoluciones.com/handle/123456789/106235

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0512337
 http://arxiv.org/abs/math/0512337

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arXiv