# Finitely Generated Algebra and Finite Extension

Suppose $L,K$ are fields. Is is true that if $L$ a finitely generated $K$-algebra then $L/K$ is a finite field extension?

Wikipedia seems to think so. But if it is true surely it's difficult to prove? After all the Nullstellensatz would seem to follow immediately from such a result. Is this the basic idea of Noether Normalisation?

You can look at my answer given here. It proves using Noether Normalisation that the extension $L/K$ must necessarily be finite.