Exercise 6, § 2

Let A be an integrally closed domain, K its field of fractions, p a prime ideal of A and k the field of fractions of A/p. Show that, if A, is not a valuation ring, there exists a valuation ring V of K which dominates A, and whose residue field is a transcendental extension of k (use Chapter V, § 2, Exercise 14 (b)).