Cofinitely δ--supplemented modules

A module M was called cofinitely δ--supplemented if for every cofinite submodule of M,exists a δ-supplement,which was a direct summand term of M.Some properties of cofinitely δ--supplemented modules were given and it was proved that if M was a cofinitely δ--supplemented module meetting the conditions(D3),then any cofinite direct summand term of M would be cofinitely δ--supplemented,and meantime,also proved that any finite direct sum of cofinitely δ--supplemented modules would be a cofinitely δ--supplemented module.