Integral Elements of $\mathbb{Q[x]}$ in $\mathbb{Q(x)}$

Asked Jan 22 '18 at 10:41

Active Jan 22 '18 at 10:49

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So I am wondering which how one can find the integral elements of $\mathbb{Q[x]}$ in its field of fractions $\mathbb{Q(x)}$.

I have shown that $\frac{p(x)}{q(x)}$ is integral iff $p(x) \in \sqrt{<q(x)>}$. Can I give a more complete characterization of the integral closure of $\mathbb{Q[x]}$?

edited Jan 22 '18 at 10:49

asked Jan 22 '18 at 10:41

Nick A.

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$\mathbb Q[x]$ is integrally closed. – user26857 Jan 22 '18 at 10:44
Could you explain why is that ? – Nick A. Jan 22 '18 at 10:51
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You can find this everywhere. Look for UFDs are integrally closed. – user26857 Jan 22 '18 at 10:52
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See https://math.stackexchange.com/questions/150554/ufds-are-integrally-closed. – lhf Jan 22 '18 at 12:39

Integral Elements of $\mathbb{Q[x]}$ in $\mathbb{Q(x)}$

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