Definition:Algebraic Field Extension

Definition
A field extension $E / F$ is said to be algebraic :
 * $\forall \alpha \in E: \alpha$ is algebraic over $F$

Also known as
An algebraic field extension can also be referred to as an algebraic extension field, or just as an algebraic extension.

Also see

 * A field extension is said to be transcendental it is not algebraic.