Multiplicative Lie-type derivations on alternative rings

Abstract

Let be an alternative ring containing a nontrivial idempotent and be a multiplicative Lie-type derivation from into itself. Under certain assumptions on we prove that is almost additive. Let be the -th commutator defined by n indeterminates If is a unital alternative ring with a nontrivial idempotent and is -torsion free, it is shown under certain condition of and that where δ is a derivation and such that for all