On the Goldie Dimension of Rings and Modules
Journal of Algebra
goldie dimension, hereditary rings, noetherian rings
Algebra | Mathematics
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.
Dinh, Hai Q.; Guilo Asensio, Pedro A.; and López-Permouth, Sergio R. (2006). On the Goldie Dimension of Rings and Modules. Journal of Algebra 305(2), 937-948. doi: 10.1016/J.JALGEBRA.2006.06.043 Retrieved from https://digitalcommons.kent.edu/mathpubs/10