Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4588553 | Journal of Algebra | 2006 | 12 Pages |
Abstract
We find a bound for the Goldie dimension of hereditary modules in terms of the cardinality of the generating sets of their quasi-injective hulls. Several consequences are deduced. In particular, it is shown that every finitely generated hereditary module with countably generated quasi-injective hull is noetherian. It is also shown that every right hereditary ring with finitely generated injective hull is right artinian, thus answering a long standing open question posed by Dung, Gómez Pardo and Wisbauer.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory