Multiplicative Lie-type derivations on alternative rings

摘要

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 p(n)(x(1), x(2), ... , x(n)) be the (n - 1)-th commutator defined by n indeterminates x(1), ... , x(n). 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 = delta + tau, where delta is a derivation and tau : R -> Z(R) such that tau(p(n)(a(1), ... , a(n))) = 0 for all a(1), ... , a(n) is an element of R.