Definition:Algebraic Field Extension

Definition

A field extension $E / F$ is said to be algebraic if and only if:

$\forall \alpha \in E: \alpha$ 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 if and only if it is not algebraic.

Sources

• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): algebraic extension (or algebraic extension field)