I think i understand the first 2 parts of the hints but the last part of this question just confuses me =/ Prove that if N is a submodule of an R module M so that the quotientM/N is a free R module then there exists a complementary submodule to N in M. lecturer's hint: let X be a subset of M st (x + N| x in X) is basis of M/N define fn B: M/N --> M st B(x +N) = x for all x in X and show that im(B) is complementary to N