Maps of modules that every closed submodules are direct summand

Let R be associative ring with identity and M be a right R-module. A module Mis called extending if every closed submodule of M is a direct summand of M.There are other equivalent definitions which they improved the theory. But on theother hand, in the development of the theory some people used different terminologywrong way some how. This make cause for new researchers. In our work, we studyall works that we could reach and based only the above definition, give the relationsamong them and show them with diagrams in the last section.