# A hint on a field extension problem?

1. Apr 6, 2013

### QIsReluctant

*** This is *not* homework. All I'd like is a push in the right direction.***

1. The problem statement, all variables and given/known data
Let $K / F$ be an algebraic field extension and $R$ a ring such that $F \subset R \subset K$. Show that $R$ is a field.
2. Relevant equations
(none)
3. The attempt at a solution
I know that every element in $R$ is algebraic over $F$ and that every element in $R \setminus{F}$ must have an inverse in $K\setminus{F}$. It suffices that these inverses are in $R\setminus{F}$, but I'm stuck trying to find a way to prove that this is the case. I've explored minimal polynomials of the inverse, but that doesn't seem to prove anything. Hrlp.

Last edited: Apr 6, 2013