论文标题
替代环上的乘法型式衍生
Multiplicative Lie-type derivations on alternative rings
论文作者
论文摘要
令$ \ r $为一个替代戒指，其中包含一个非平凡的愿望，$ \ d $是从$ \ r $进入自身的乘法lie-type派生。根据$ \ r $的某些假设，我们证明$ \ d $几乎是加性的。令$ p_n（x_1，x_2，\ cdots，x_n）$为$（n-1）$ - $ n $ nodemerminates $ x_1，\ cdots，x_n $定义的换向器。如果$ \ r $是具有非平凡性的Unital替代戒指，则是$ \ {2,3，n-1，n-3 \} $ - 不含扭矩，它在某些条件下显示为$ \ r $和$ \ d $，$ \ d =δ+τ$ a $δ$ a deDevation and perivation and perivation and derivation and col。 z}（\ r）$使得$τ（p_n（a_1，\ ldots，a_n））= 0 $ for All $ a_1，\ ldots，a_n \ in \ r $。
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 $\D=δ+τ$, where $δ$ is a derivation and $τ\colon\R\longrightarrow{\mathcal Z}(\R)$ such that $τ(p_n(a_1,\ldots,a_n))=0$ for all $a_1,\ldots,a_n\in\R$.
