Definition:Integral Element of Ring Extension

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

Let $R \subseteq A$ be a subring.

Then $a \in A$ is said to be integral over $R$ is is a root of a monic nonzero polynomial over $R$.

Also see

 * Equivalence of Definitions of Integral Dependence
 * Definition:Integral Element of Algebra
 * Definition:Integral Ring Extension
 * Definition:Algebraic Element of Field Extension