Definition:Integral Element of Algebra/Definition 3

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

Let $f : A \to B$ be a commutative $A$-algebra.

Let $b \in B$.

The element $b$ is integral over $A$ the generated subalgebra $A \sqbrk b$ is contained in a subalgebra $C \le B$ which is a finitely generated module over $A$.

Also see

 * Equivalence of Definitions of Integral Element of Algebra