Lie Algebras of Locally Finite Derivations over Fields of Positive Characteristic

Let $F$ be a field of positive characteristic, and let $A$ be a finitely generated commutative associative $F$-algebra. We study Lie subalgebras of $DerA$ generated by locally finite derivations. We prove that if all commutators of the generators satisfy a natural local finiteness condition, then the associative subalgebra of $En{d}_{F}A$ generated by these derivations is finite-dimensional.