COPURE INJECTIVE MODULES

Abstract

A module is said to be copure injective if it is injective with respect to all modules A ⊂ B with B/A injective. We first characterize submodules that have the extension property with respect to copure injective modules. Then we characterize commutative rings with finite self injective dimension in terms of copure injective modules. Finally, we show that the quotient categories of reduced copure injective modules and reduced h- divisible modules are isomorphic.