MODULES WHICH ARE INVARIANT UNDER AUTOMORPHISMS OF THEIR INJECTIVE HULLS

A module is defined to be an automorphism-invariant module if it is invariant under automorphisms of its injective hull. Quasi-injective modules and, more generally, pseudo-injective modules are all automorphism-invariant. Here we develop basic properties of these modules, and discuss when an automorphism-invariant module is quasi-injective or injective. Some known results on quasi-injective and pseudo-injective modules are extended.