Definition:Normal Extension/Definition 2

Definition
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 :
 * $\map \sigma L = L$

for each $\sigma \in \Gal {L / K}$.

Also see

 * Equivalence of Definitions of Normal Extension