Small annihilator maximal sub-modules

The main objective of this work is to present and study a new generalization of annihilator maximal sub modules that is small annihilator maximal sub modules. We are investigated the relationship between Maximal Annihilator Maximal Sub modules with Small Annihilator Maximal Sub modules. In addition, we are introduced the concept of Small Annihilator Semi-Simple Modules which serve as generalization of Annihilator Semi-Simple Modules. Many of the basic properties and descriptions of these ideas are discussed. In addition, their relationship to other related concepts is studied.