Definition. splitting field [1502]

Let $F$ be a field and $f(x) \in F[x]$. A field extension $K$ of $F$ is called a splitting field for $f(x)$ (over $F$) if

1. $f(x)$ splits completely in $K[x]$,
2. $f(x)$ does not split complete in $E[x]$ for any subfield $E \subsetneq K$ containing $F$. (Or equivalently, if $F \subseteq E \subseteq K$ and $f(x)$ splits complete over $E$, then $E = K$.)