关于素环平方封闭的李理想的两个结果

Two Results on Square Closed Lie Ideals of Prime Rings

中文关键词:  素环  李理想  导子  广义导子.

英文关键词:prime ring  Lie ideal  derivation  generalized derivation.

中文摘要:

      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.

英文摘要:

      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 $U\subseteq Z(R)$.