ON HOLLOW-WEAK LIFTING MODULES

Let R be any ring and let M be any right R-module. M is called hollow-weak lifting if every semisimple submodule N of M such that M/N is hollow has a cossential submodule that is a direct submmand of M. We prove that M is hollow-weak lifting iff every semisimple N of M such that M/N is hollow has strong supplemented in M.And show that M is hollow-weak lifting iff every semisimple submodule N of M such that M/N is hollow can be written as N=KoplusL with K is direct summand of M and L is small submodule of M.