Definition:Integral Element of Algebra/Definition 1

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 $A$ it is a root of a monic polynomial in $A[x]$.

Also see

 * Equivalence of Definitions of Integral Element of Algebra