  We establish a Primitive Element Theorem for fields equipped with several
commuting operators such that each of the operators is either a derivation or
an automorphism. More precisely, we show that for every extension $F \subset E$
of such fields of zero characteristic such that
  $\bullet$ $E$ is generated over $F$ by finitely many elements using the field
operations and the operators,
  $\bullet$ every element of $E$ satisfies a nontrivial equation with
coefficient in $F$ involving the field operations and the operators,
  $\bullet$ the action of the operators on $E$ is irredundant there exists an
element $a \in E$ such that $E$ is generated over $F$ by $a$ using the field
operations and the operators.
  This result generalizes the Primitive Element Theorems by Kolchin and Cohn in
two directions simultaneously: we allow any numbers of derivations and
automorphisms and do not impose any restrictions on the base field $F$.
