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Say $R$ is an integral domain with field of fractions $F$. Further, say there is an $R'$ (integral domain) such that $R\subset R'\subset F$. We want to prove that the field of fractions $F'$ of $R'$ is isomorphic to $F$.

I was thinking something along the lines, let $x,y\in R'$ with $y\neq 0$. Then $x,y\in F$, so $\frac{x}{y}\in F$ since the localization of $F$ is $F$ itself. Hence, $F'\subset F$. Also, since $R\subset R'$ we ought to have $F\subset F'$ and hence, $F=F'$.

Why is the question asking for isomorphic. I think that equality ought to hold. Am I doing something wrong?

Thanks

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    Thank you. I was thinking the same thing. I think its just a matter of technicalities.2012-11-08

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