## You are here

Homeintegrity characterized by places

## Primary tabs

# integrity characterized by places

###### Theorem.

Corollary 1. Let $R$ be a subring of the field $K$, $1\in R$. The integral closure of $R$ in $K$ is the intersection of all valuation domains in $K$ which contain the ring $R$. The integral closure is integrally closed in the field $K$.

Corollary 2. Every valuation domain is integrally closed in its field of fractions.

Keywords:

integral over a ring

Related:

Integral, PlaceOfField

Major Section:

Reference

Type of Math Object:

Theorem

Parent:

## Mathematics Subject Classification

12E99*no label found*13B21

*no label found*

- Forums
- Planetary Bugs
- HS/Secondary
- University/Tertiary
- Graduate/Advanced
- Industry/Practice
- Research Topics
- LaTeX help
- Math Comptetitions
- Math History
- Math Humor
- PlanetMath Comments
- PlanetMath System Updates and News
- PlanetMath help
- PlanetMath.ORG
- Strategic Communications Development
- The Math Pub
- Testing messages (ignore)

- Other useful stuff

## Recent Activity

Jul 5

new correction: Error in proof of Proposition 2 by alex2907

Jun 24

new question: A good question by Ron Castillo

Jun 23

new question: A trascendental number. by Ron Castillo

new correction: Error in proof of Proposition 2 by alex2907

Jun 24

new question: A good question by Ron Castillo

Jun 23

new question: A trascendental number. by Ron Castillo