# integrally closed

A subring $R$ of a commutative ring $S$ is said to be 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 IntegrallyClosed 2013-03-22 12:36:34 2013-03-22 12:36:34 rmilson (146) rmilson (146) 15 rmilson (146) Definition msc 13B22 msc 11R04 normal ring IntegralClosure AlgebraicClosure AlgebraicallyClosed