Multiplicative Lie-type derivations on alternative rings

Abstract

Let R be an alternative ring containing a nontrivial idempotent and D be a multiplicative Lie-type derivation from R into itself. Under certain assumptions on R, we prove that D is almost additive. Let pn(x1,x2,…,xn) be the (n−1)-th commutator defined by n indeterminates x1,…,xn. If R is a unital alternative ring with a nontrivial idempotent and is {2,3,n−1,n−3}-torsion free, it is shown under certain condition of R and D that D=δ+τ, where δ is a derivation and τ:R→Z(R) such that τ(pn(a1,…,an))=0 for all a1,…,an∈R.