# Definition:Transcendental Field Extension

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## 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.