Multiplicative Lie-type derivations on alternative rings

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