Title

On the Goldie Dimension of Rings and Modules

Publication Title

Journal of Algebra

Publication Date

2006

Document Type

Article

DOI

10.1016/J.JALGEBRA.2006.06.043

Keywords

goldie dimension, hereditary rings, noetherian rings

Disciplines

Algebra | Mathematics

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.

Publisher

Elsevier

Publisher Location

Amsterdam, Netherlands


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