MODULES INVARIANT UNDER AUTOMORPHISMS OF THEIR ENVELOPES

Abstract

This article introduces the concept of X- envelopes, which can be seen as the general concept of the injective envelopes and gives some of its properties similar to the case of injective envelopes. In addition, the study also introduces the concept of modules invariant under automorphisms of their envelopes as a generalization of automorphisms invariant modules and gives some similar results. The purpose of the article is to review recent results to prepare the writer's study.

Keywords: X- envelope, X- injective envelope, X-automorphisms,       X-endomorphisms