If $R\subseteq S$ are commutative rings, an element $s\in S$ is **integral** over $R$ if there exists $n\in\Z^+$ and $a_i\in R$ such that
$$ s^n+a_{n-1} s^{n-1}+\cdots + a_0 =0\,.$$

The **integral closure** of $R$ in $S$ is $\{s\in S\mid s \text{ is integral over } R\}$.

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**Knowl status:**

- Review status: reviewed
- Last edited by John Voight on 2020-10-23 11:18:36

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**History:**(expand/hide all)

- 2020-10-23 11:18:36 by John Voight (Reviewed)
- 2018-08-06 14:56:01 by John Jones (Reviewed)

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