Multiplicative Lie-type derivations on alternative rings

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 \(p_n(x_1, x_2, \cdots, x_n)\) be the \((n-1)\)-th commutator defined by \(n\) indeterminates \(x_1, \cdots, x_n\). 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 \(\tau\colon\R\longrightarrow{\mathcal Z}(\R)\) such that \(\tau(p_n(a_1,\ldots,a_n))=0\) for all \(a_1,\ldots,a_n\in\R\).