Multiplicative Lie-type derivations on alternative rings

Let $\mathbb{R}$ be an alternative ring containing a nontrivial idempotent and $\text{D}$ be a multiplicative Lie-type derivation from $\mathbb{R}$ into itself. Under certain assumptions on $\mathbb{R}$, we prove that $\text{D}$ is almost additive. Let $p_n(x_1, x_2, \cdots, x_n)$bethe$(n-1)$-thcommutatordefinedby$n$indeterminates$x_1, \cdots, x_n$\mathrm{.}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 $\mathbb{R}$ and $\text{D}$, that $\text{D}=\delta +\tau$, where $\delta$ is a derivation and $\tau \text{\hspace{0.17em}⁣}:\mathbb{R}⟶\mathcal{Z}(\mathbb{R})$ such that $\tau (p_n(a_1,\dots ,a_n))=0$ for all $a_1,\dots ,a_n\in \mathbb{R}$.