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Skew Derivations with Central Invariants

If σ is an automorphism and δ is a σ‐derivation of a ring R, then the subring of invariants is the set R(δ)={r∈R∣δ(r)=0}. The main result of this paper is ‘let R be a semiprime ring with an algebraic σ‐derivation δ such that R(δ) is central; then R is commutative’. This theorem generalizes results on the invariants of automorphisms and derivations and is proved by reducing down to the special cases of automorphisms and derivations.