Supplement -Hollow and Supplement-Lifting Modules

The principle idea of our work is to present newly generalization for two major types of modules, which are hollow module and lifting module they are supplement –hollow module and supplement –lifting module respectively. We consider supplement - hollow module as. Let be a non-zero unital left -module and be a ring with identity then C is known as the supplement-hollow module ( indicates sp-hollow). If each proper submodule of is a supplement small submodule in . Furthermore, an -module is known as supplement –lifting module (indicates sp lifting).If there is a submodule H of for each sub module of such as and ,where L is a submodule of C. After studying these ideas, we came up with some connected findings