Here's the problem:

Let K be an algebraically closed field. Show any isomorphism of K onto a subfield of K such that K is algebraic over is an automorphism of K, that is show .

I know can be extended to an isomorphism where K'<=K. And since K<=K'<=K we know can only be extended to an automorphism of K. But does this help me? I don't see how to make the connection with .

Any advice would be great! :-)