# Definition:Field Extension/Degree

## Definition

Let $E / F$ be a field extension.

The degree of $E / F$, denoted $\index E F$, is the dimension of $E / F$ when $E$ is viewed as a vector space over $F$.

### Finite

$E / F$ is a finite field extension if and only if its degree $\index E F$ is finite.

### Infinite

$E / F$ is an infinite field extension if and only if its degree $\index E F$ is not finite.