\begin{definition}[Definition:Integral Element of Algebra/Definition 4]
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 $A$ {{iff}} there exists a faithful $A \sqbrk b$-module whose restriction of scalars to $A$ is finitely generated.
\end{definition}