Exercise 7, § 3

Let A be a ring and $(S_\lambda)_{\lambda \in L}$ a family of multiplicative subsets of A such that, for every maximal ideal m of A, there exists $A \in L$ such that $m \cap S_\lambda = \varnothing$ (cf. § 2, Exercise 8). Let M, N be two A-modules and $u : M \to N$ a homomorphism. For u to be surjective (resp. injective, bijective, zero), it is necessary and sufficient that, for all $A \in L$, $S_\lambda^{-1}u : S_\lambda^{-1}M \to S_\lambda^{-1}N$ be so. How can the Corollaries to Theorem 1 of no. 3 be generalized?