Definition:Transcendental (Abstract Algebra)/Field Extension

Definition
A field extension $E / F$ is said to be transcendental iff:
 * $\exists \alpha \in E: \alpha$ is transcendental over $F$

That is, a field extension is transcendental if it contains at least one transcendental element.

Also see
If no element of $E / F$ is transcendental over $F$, then $E / F$ is algebraic.