Abstract: | Let be a finitely generated commutative domain over an algebraically closed field , an algebra endomorphism of , and a -derivation of . Then if and only if is locally algebraic in the sense that every finite dimensional subspace of is contained in a finite dimensional -stable subspace. Similarly, if is a finitely generated field over , a -endomorphism of , and a -derivation of , then if and only if is an automorphism of finite order. |