Lüroth field extensions

Theorem 2. Suppose, in addition, that K is an algebraically closed field. Let R be a K-subalgebra of the fieldK(x1,…,xn)that is integrally closed inK(x1,…,xn)and the transcendence degree of its field of fractionsQ(R)is 1 over K. Then there exists a transcendental elementx∈Rover K such thatK[x]⊆R⊆K(x)=Q(R).