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# 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

Type of Math Object:

Theorem

Major Section:

Reference

Parent:

Groups audience:

## Mathematics Subject Classification

12E99*no label found*13B21

*no label found*

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