This page contains a result which it refers to as the UFD field lemma. I was wondering if anybody knew of any other references which discuss this result--this page is the only place I've seen it.
The UFD field lemma appears to assert that if $R$ is a unique factorization domain containing infinitely many prime elements, if $F$ is the field of fractions of $R$, and if $A$ is a finitely generated $R$-algebra which is a field and is algebraic over $F$, then $A$ does not contain $F$.
I'm looking for other sources because I find the exposition on that page a little hard to follow.