# Definition:Integral Closure

## Definition

Let $A$ be an extension of a commutative ring with unity $R$.

Let $C$ be the set of all elements of $A$ that are integral over $R$.

Then $C$ is called the **integral closure** of $R$ in $A$.

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Let $A$ be an extension of a commutative ring with unity $R$.

Let $C$ be the set of all elements of $A$ that are integral over $R$.

Then $C$ is called the **integral closure** of $R$ in $A$.

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