Definition:Field Extension/Degree

Definition
Let $E / F$ be a field extension.

The degree of $E / F$, denoted $\left[{E : F}\right]$, is the dimension of $E / F$ when $E$ is viewed as a vector space over $F$.

Also see

 * Definition:Finite Field Extension: where $\left[{E : F}\right]$ is finite
 * Definition:Infinite Field Extension: where $\left[{E : F}\right]$ is not finite