$σ$ -素环上的中心化自同构与Jordan左导子
Centralizing automorphisms and Jordan left derivations on $σ$-prime rings
摘要：
设$R$是2-挠自由$σ$ -素环.本文证明了：如果$U\not\subset Z(R)$是$R$和$R$中的$a, b$的$σ$ -Lie理想，使得$aUb=σ(a)Ub=0,$，则要么是$a=0$，要么是$b=0.$.最后，我们描述了可加映射$d: R \longrightarrow R$使得$d(u^2) = 2ud(u)$，其中$u\in U,$是$R.$的非零$σ$ -平方闭李理想
英文摘要：
Let $R$ be a 2-torsion free $σ$-prime ring. It is shown here that if $U\not\subset Z(R)$ is a $σ$-Lie ideal of $R$ and $a, b$ in $R$ such that $aUb=σ(a)Ub=0,$ then either $a=0$ or $b=0.$ This result is then applied to study the relationship between the structure of $R$ and certain automorphisms on $R$. To end this paper, we describe additive maps $d: R \longrightarrow R$ such that $d(u^2) = 2ud(u)$ where $u\in U,$ a nonzero $σ$-square closed Lie ideal of $R.$
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