Skew derivations with algebraic invariants of bounded degree

This paper examines semiprime algebras A with a q-skew σ-derivation δ, where both δ and σ   are algebraic. With minor assumptions on the ground field, we show that if the invariants AδAδ are algebraic of bounded degree, then A must be finite dimensional. As an application, it is shown that if A is a semiprime Banach algebra and δ   is continuous, then whenever AδAδ is algebraic, it follows that A is finite dimensional.