Exercise 3, § 2

Let $A$ be an integral ring of dimension 1, and let $p_0 \subset p_1 \subset p_2$ be three distinct non-zero prime ideals of $A[X]$. Now prove that $p_0 \cap A = {0}$, $p_1 = (p_1 \cap A).A[X]$, and that $p_2$ is a maximal ideal of $A[X]$.