1. Open Access Kent State
  2. On the Goldie Dimension of Rings and Modules
Author(s)
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.
Format
Article
Identifier(s)
10.1016/J.JALGEBRA.2006.06.043
Publication Date
2006-01-01
Publication Title
Elsevier
Volume
305
Issue
2
First Page
937
Last Page
948
Keywords
Subject
Community
Department of Mathematical Sciences
Permalink https://oaks.kent.edu/mathpubs/10
Dinh, H., Asensio, P., & López-Permouth, S. (2006). On the Goldie Dimension of Rings and Modules. Elsevier. https://doi.org/10.1016/J.JALGEBRA.2006.06.043
Dinh, Hai, Pedro Asensio, and Sergio López-Permouth. 2006. “On the Goldie Dimension of Rings and Modules”. Elsevier. https://doi.org/10.1016/J.JALGEBRA.2006.06.043.
Dinh, H., P. Asensio, and S. López-Permouth. On the Goldie Dimension of Rings and Modules. Elsevier, 1 Jan. 2006, doi:10.1016/J.JALGEBRA.2006.06.043.