On the Goldie dimension of rings and modules

JOURNAL OF ALGEBRA

卷:305

Article

Dinh, Hai Q. ; Asensio, Pedro A. Guil ; Lopez-Permouth, Sergio R.

关键词: Goldie dimension;    hereditary rings;    Noetherian rings;   

DOI  :  10.1016/j.jalgebra.2006.06.043

来源: Elsevier

【 摘 要 】

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, Gomez Pardo and Wisbauer. (c) 2006 Elsevier Inc. All rights reserved.

【 授权许可】

Free