PlanetMath: integrally closed

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integrally closed

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A subring of a commutative ring is said to be integrally closed in if whenever $\theta \in S$ and $\theta$ is integral over , then $\theta \in R$ .

The integral closure of in is integrally closed in .

An integral domain is said to be integrally closed (or normal) if it is integrally closed in its fraction field.

"integrally closed" is owned by rmilson. [ full author list (2) | owner history (1) ]

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Other names:

normal ring

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Cross-references: fraction field, integral domain, integral closure, integral, commutative ring, subring
There are 19 references to this entry.

This is version 12 of integrally closed, born on 2002-04-23, modified 2007-07-27.
Object id is 2867, canonical name is IntegrallyClosed.
Accessed 4220 times total.

Classification:

AMS MSC:	11R04 (Number theory :: Algebraic number theory: global fields :: Algebraic numbers; rings of algebraic integers)
	13B22 (Commutative rings and algebras :: Ring extensions and related topics :: Integral closure of rings and ideals ; integrally closed rings, related rings )

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