Exercise 10, § 3

Let A, B be two rings, $\rho : A \to B$ a homomorphism, q a prime ideal of B and $p = \rho^{-1}(q)$. Suppose that there exists a B-module N such that $N_q$ is a flat A-module which is not reduced to 0 and $N_p$ is a finitely generated A,-module; then the prime ideal p is minimal in A. (Observe that $N_p$ is then a faithfully flat $A_p$-module and use Corollary 4 to Proposition 11 of § 2, no. 5.)