How to show that $R$ is a PID if $\mathbb{Z}\subset R\subset \mathbb Q$?
I tried as follows:
Let $I$ be an ideal in $R$. Then $\mathbb Z\cap I$ is an ideal in $\mathbb Z$. But I couldn't proceed further. Please help.
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Anupam
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Particular case of http://math.stackexchange.com/questions/137876/a-subring-of-the-field-of-fractions-of-a-pid-is-a-pid-as-well You can also use some ideas from http://math.stackexchange.com/questions/570619/subrings-of-rationals-are-noetherian – Nov 19 '13 at 17:17