Definition:Integral Ring Extension

Definition
Let $A$ be a commutative ring with unity.

Let $R\subset A$ be a subring.

The ring extension $R \subseteq A$ is said to be integral for all $a \in A$, $a$ is integral over $R$.

Also known as
An integral ring extension can also be referred to as an integral extension.

Also see

 * Definition:Integral Closure
 * Definition:Algebraic Field Extension