2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/106235We find a bound for the Goldie dimension of hereditary modules in terms of the cardinality of the generator sets of its quasi-injective hull. Several consequences are deduced. In particular, it is shown that every right hereditary module with countably generated quasi-injective hull is noetherian. Or that every right hereditary ring with finitely generated injective hull is artinian, thus answering a long standing open question posed by Dung, Gomez Pardo and Wisbauer.13 pagesRings and Algebras16D50; 16D90; 16L30text