Definition:Transcendental Field Extension
Jump to navigation
Jump to search
Definition
A field extension $E / F$ is said to be transcendental if and only if:
- $\exists \alpha \in E: \alpha$ is transcendental over $F$
That is, a field extension is transcendental if and only 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.
Historical Note
The term transcendental, in the sense of meaning non-algebraic, was introduced by Gottfried Wilhelm von Leibniz.
