There are no Keller maps having prime degree field extensions

The two-dimensional Jacobian Conjecture says that a Keller map $f:(x,y)\mapsto (p,q)\in k[x,y{]}^2$ having an invertible Jacobian is an automorphism of $k[x,y]$. We prove that there is no Keller map with $[k(x,y):k(p,q)]$ prime.