The distribution of prime divisors in finitely generated domains (Q1963831)

Let \(R\) be an integral domain which is a finitely generated \(k\)-algebra over a field \(k\), and let \(L\) be the quotient field of \(R\). In this paper, the author investigates when each divisor class in the class group \(Cl(R)\) contains a prime divisor. The main results are that each divisor class contains infinitely many prime divisors if either (1) \(k\) is a Hilbertian field and \(L\) is separable and transcendental over \(k\), or (2) \(k\) is infinite, \(L\) is separable over \(k\), and \(\dim\geq 2\).