If $R$ is an integral domain, show that there is no subfield $k$ of Frac($R$) containing $R$.
I think the way to prove this is by contradiction. So, let $R$ be an integral domain, and let $k$ be a subfield of Frac($R$) such that $R$$\subseteq \!\,$$k$. I think we need to assume that two elements are in $k$ and then show that at least one of these elements is not in $R$. So, to show that two elements are not in $R$, we need the product of these two elements to equal zero.
Let $h$,$j$ $\in \!\ k$. I am honestly not sure what to do from here.