Exercise 3, § 2

Let c be a cardinal and P a projective A-module such that $\gamma(P) \leq c$ (§ 1,

Exercise 6). Show that if L is a free A-module with an infinite basis of cardinal $\geq c$, $P \oplus L$ is isomorphic to L. (Observe that there exists a free A-module M, whose basis has cardinal $\leq c$, isomorphic to the direct sum of P and an A-module Q. Note that $M^{(N)}$ and $P \oplus M^{(N)}$ are isomorphic.)