integrally closedIntegrallyClosed2002-04-23 17:03:172007-07-27 05:19:47Definition% this is the default PlanetMath preamble. as your knowledge
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% define commands hereA subring $R$ of a commutative ring $S$ is said to be {\em integrally closed} in $S$ if whenever $\theta \in S$ and $\theta$ is integral over $R$, then $\theta \in R$.
The integral closure of $R$ in $S$ is integrally closed in $S$.
An integral domain $R$ is said to be {\em integrally closed} (or {\em \PMlinkescapetext{normal}}) if it is integrally closed in its fraction field.