Isomorphisms between injective modules

Suppose that [Formula: see text] is an injective structure of [Formula: see text]-Mod such that the class [Formula: see text] is closed for direct limits, then two modules in [Formula: see text] are isomorphic if there are maps in [Formula: see text] from each one of the modules into the other. Examples of module classes in such injective structures include (pure, coneat and RD-) injective modules. The idea of injective structures is slightly generalized to include [Formula: see text]-injective modules for a hereditary torsion theory [Formula: see text], as well. Thus providing a generalization of a classical result of Bumby’s and two recent ones by Macías-Díaz.