On the cancellation problem of Zariski

Abstract

Let K-1 and K-2 be extension fields over a field K with charK = p > 0. Assume L = K-1(x(1)) = K-2(x(2)) > K where x(i) is transcendental over K-i, for i = 1,2. In this paper we prove that if K-1 is a perfect field, then K-1 = K-2.