Modules characterized with some special submodules

For an associative ring R with identitiy, let M be a right R-module. If every complement submodule of M is a direct summand of M, then M is called CS-module. Extending module, CS-module and a module which satisfy C_1 property are all equivalent. But in the development of the theory, there are several different definitions of this kind of modules had been work by some researchers and also published as a survey( see DoĞruöz, S., Ürün, Ö. 2012. Surveys in Mathematics and Mathematical Sciences, 1(2):117-162). In this work we study all different definitions that we access them in the sense of CS-modules characterized by complement submodules and give relations among them.