\begin{definition}[Definition:Normal Extension/Definition 2]
Let $L / K$ be a field extension.
Let $\overline K$ be the algebraic closure of $K$.
Let $\Gal {L / K}$ denote the set of embeddings of $L$ in $\overline K$ which fix $K$ pointwise.
Then $L / K$ is a '''normal extension''' {{iff}}:
: $\map \sigma L = L$
for each $\sigma \in \Gal {L / K}$.
\end{definition}