finite dimensional integral domain containg $\mathbb C$ Let $ R$ be an integral domain containing $\mathbb C$.
Suppose that $R$ is a finite dimensional $\mathbb C$-vector space . Show that $R=\mathbb C$.
One side $\mathbb C \subset R$ is obvious. What about the other?
Show me right way.Thanks in advance.

Hint: If it's finite dimensional, over $\mathbb{C}$, then it must be a field. This follows from integrality, or more simply just write down a polynomial killing any non-zero element of $R$, and show how you can make an inverse from this equation.
