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 $F$.

Also see

 * Definition:Finite Field Extension: where $\index E F$ is finite
 * Definition:Infinite Field Extension: where $\index E F$ is not finite
 * Definition:Separable Degree
 * Definition:Inseparable Degree