On the Goldie Dimension of Hereditary Rings and Modules
Rings and Algebras
2007-05-23 v1
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.
Keywords
Cite
@article{arxiv.math/0512337,
title = {On the Goldie Dimension of Hereditary Rings and Modules},
author = {H. Q. Dinh and P. A. Guil Asensio and S. R. Lopez-Permouth},
journal= {arXiv preprint arXiv:math/0512337},
year = {2007}
}
Comments
13 pages