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 $A$.

Also see

 * Integral Closure is Subring
 * Definition:Integrally Closed
 * Definition:Algebraic Closure