let r be a ring. an r-module m is called slightly compressible if, for every non-zero sub module n of m, there exists a non-zero homomorphism from m to n . we shall call a non-zero right r-module m a weak generator for mod-r if, for each non-zero right r-module x, there exists a non-zero homomorphism from m to x . we have two main purpose in this thesis . as first purpose, we give conditio that an r-module m become slightly comressible , and as second purpose , we research conditions that a non-zero right r-module become weak generator for mod-r .