Definition:Field Extension

Definition
Let $F$ be a field.

A field extension over $F$ is a field $E$ where $F \subseteq E$.

That is, such that $F$ is a subfield of $E$.

This can be expressed:
 * $E$ is a field extension over a field $F$

or:
 * $E$ over $F$ is a field extension

as:
 * $E / F$ is a field extension.

$E / F$ can be voiced as $E$ over $F$.

Also see

 * Definition:Tower of Fields