integrally closed

A subring $R$ of a commutative ring $S$ is said to be 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 integrally closed (or ) if it is integrally closed in its fraction field.

Title	integrally closed
Canonical name	IntegrallyClosed
Date of creation	2013-03-22 12:36:34
Last modified on	2013-03-22 12:36:34
Owner	rmilson (146)
Last modified by	rmilson (146)
Numerical id	15
Author	rmilson (146)
Entry type	Definition
Classification	msc 13B22
Classification	msc 11R04
Synonym	normal ring
Related topic	IntegralClosure
Related topic	AlgebraicClosure
Related topic	AlgebraicallyClosed