Invariance Of Modules Under Automorphisms Of Their Envelopes And Covers

"The study of modules which are invariant under the action of certain subsets of the endomorphism ring of their injective envelope can be drawn back to the pioneering work of Johnson and Wong in which they characterized quasi-injective modules as those modules which are invariant under any endomorphism of their injective envelope. Later, Dickson and Fuller studied modules which are invariant under the group of all automorphisms of their injective envelope and proved that any indecomposable automorphism-invariant module over an F-algebra A is quasi-injective provided that F is a field with more than two elements. But after that this topic remained in dormant stage for some time until Lee and Zhou picked it up again in their paper where they called such modules auto-invariant modules. But the major breakthrough on this topic came from two papers that appeared a few months later: one of them was a paper of Er, Singh and Srivastava where they proved that the automorphism-invariant modul