\begin{definition}[Definition:Integral Element of Algebra/Definition 2]
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}} the generated subalgebra $A \sqbrk b$ is a finitely generated module over $A$.
\end{definition}