Two Results on Square Closed Lie Ideals of Prime Rings

DOI：10.3770/j.issn:1000-341X.2010.01.016

 作者 单位 黄述亮 滁州学院数学系,安徽 滁州 239012 傅士太 南京师范大学数学与计算机科学学院, 江苏 南京 210097

设$d_{1}$是2-扭自由的素环$R$的非零导子, $\gamma$ 是伴随$d_{2}$非零的$R$的广义导子, $U$是$R$的一个平方封闭的李理想. 本文证明如果$[d_{1}^{2}(u),u]\in Z(R)$ 或$\gamma$ 同态(或反同态)作用于$U$,那么$U$ 是中心李理想.

Let $R$ be a $2$-torsion free prime ring, $d_{1}$ a nonzero derivation, $\gamma$ a generalized derivation associated with a nonzero derivation $d_{2}$, $U$ a square closed Lie ideal of $R$. In the present paper, we prove that if $[d_{1}^{2}(u),u]\in Z(R)$ or $\gamma$ acts as a homomorphism (or an antihomomorphism) on $U$, then $U\subseteq Z(R)$.