Torsion theoretic dimensions and relative Gabriel correspondence

Let τ be an hereditary torsion theory. For a ring with τ-Gabriel dimension, we find necessary and sufficient conditions for the existence of a bijective correspondence between the τ-torsionfree injective modules and the τ-closed prime ideals. As an application, new characterizations of fully bounded noetherian rings are obtained. © 2002 Elsevier Science B.V. All rights reserved.