Definition. splitting field for $A$ [2202]

Let $F$ be a field and $A$ be a subset of $F[x]$. An algebraic field extension $K$ of $F$ is called a splitting field for $A$ (over $F$) if

1. every $f(x) \in A$ splits completely in $K[x]$
2. if $F \subseteq L \subseteq K$ and every $f(x) \in A$ splits completely in $L[x]$, then $L = K$.