normal extension

A field extension $K/F$ is normal if every irreducible polynomial $f\in F[x]$ which has at least one root in $K$ splits (factors into a product of linear factors) in $K[x]$.

An extension $K/F$ of finite degree is normal if and only if there exists a polynomial $p\in F[x]$ such that $K$ is the splitting field for $p$ over $F$.