2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/65034Suppose B is an ultraproduct of finite dimensional C^\ast-algebras. We consider mapping and injectability properties for separable C^\ast-algebras into B. In the case of approximately finite C^\ast-algebras, we obtain a classification of these mappings up to inner conjugacy. Using a Theorem of Voiculescu, we show that for nuclear C^\ast-algebras injectability into an ultraproduct of finite dimensional C^\ast-algebras is equivalent to quasidiagonality.18 pages Revised introduction, bibliography. Added other correctionsOperator AlgebrasLogic47L40; 46L07; 26E35text