ABSTRACT
The two previous chapters have left us in a pleasant position. We can draw some substantial conclusions about the structure of projective modules with virtually no effort. Since a projective module is a direct summand of a free module and a free module is certainly a coproduct of countably-generated modules (even cyclic modules), Theorem 8 yields the following result.
THEOREM 9. For any ring R, every projective left R-module is a direct sum of countably-generated submodules.
