\begin{definition}[Definition:Field Extension]
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 $F$'''.
\end{definition}