Exercise 7, § 3

Let A be a local, integral, noetherian, non-catenary ring of dimension 3 (Exercise 16, p. 83), p ⊂ A a prime ideal such that ht(p) = 1, dim(A/p) = 1. Prove that there exists an element x ∈ p such that p is minimal among the prime ideals containing Ax. Deduce that V(x) has an irreducible component of dimension 1.