Exercise 8, § 1

Let $A$ be a Krull domain; show that, for every set $I$, the polynomial ring $A[X_i]_{i \in I}$ is a Krull domain. (Observe that, if $B$ is a Krull domain, the valuations induced on $B$ by the essential valuations of $B[X_1, \ldots, X_n]$ are the essential valuations of $B$.)