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 $R$ if and only if 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