Exercise 4, § 2

Let $A$ be a Noetherian ring, $\rho : A \to B$ a ring homomorphism making $B$ into a finitely generated $A$-module and $N$ a finitely generated $B$-module. Show that the prime ideals $p \in \operatorname{Ass}(\rho_*(N))$ are the inverse images under $\rho$ of the prime ideals $q \in \operatorname{Ass}(N)$.