integrally closed

A subring R of a commutative ring S is said to be integrally closedMathworldPlanetmath in S if whenever θS and θ is integral over R, then θR.

The integral closureMathworldPlanetmath of R in S is integrally closed in S.

An integral domainMathworldPlanetmath 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