In this note all rings are associative with identity and all modules are unital right Modules unless otherwise specified. Let R be a ring and M a right R -module. It is shown that: (1) M is Artinian if and only if M is a generalized amply supplemented module and satisfies descending chains conditions on generalized supplement submodules and on small submodules; (2) if M satisfies ascending chains conditions on small submodules, then M is a lifting module if and only if M is a generalized amply supplemented module and every generalized supplement submodule is a direct summand of M. M if and only if M satisfies ( ); (3) R is semilocal if and only if every cyclic module is a generalized weakly supplemented module.