Exercise 14, § 1

Let $A$ be a Krull domain and $S$ a saturated multiplicative subset of $A$ not containing $0$ (Chapter II, § 2, Exercise 1). Show that, if the canonical homomorphism : $C(A) \to C(S^{-1}A)$ (no. 10, Proposition 17) is bijective, $S$ is generated by a family (p_i) of elements such that each $Ap_i$ is a prime ideal (note that every divisorial prime ideal which meets S is principal),