ON REFINABLE MODULES

We study on cofinitely (strong) refinable modules as a proper generalization of (strongly)  refinable modules. In  this paper various properties of these modules  are developed. It is shown that  (1) every (cofinite) direct summand of a (cofinitely) refinable module is (cofinitely) refinable; (2) a module is cofinitely refinable if and only if every cofinite direct summands lift modulo every submodule of ; (3) a ring  is Rad-supplemen-ted and left refinable if and only if it is semiperfect; (4) a semilocal ring  is a left and right artinian serial ring with  if and only if every left -module is strongly refinable. 2010 Mathematics Subject Classification. 16D10,16D40. Key words and phrases. (strongly) refinable module,  cofinitely (strong) refinable module, semiperfect ring