Annihilators and Power Values of Generalized Skew Derivations on Lie Ideals

Canadian mathematical bulletin

Vincenzo De Filippis¹ 

[1] Department of Mathematics and Computer Science, University of Messina, 98166, Messina, Italy

关键词: generalized skew derivation;    prime ring;   

DOI  :  10.4153/CMB-2015-077-x

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

Let $R$ be a prime ring of characteristic different from$2$, $Q_r$ be its right Martindale quotient ring and$C$ be its extended centroid. Suppose that $F$ isa generalized skew derivation of $R$, $L$ a non-central Lie idealof $R$, $0 eq ain R$,$mgeq 0$ and $n,sgeq 1$ fixed integers. If [aiggl(u^mF(u)u^niggr)^s=0]for all $uin L$, then either $Rsubseteq M_2(C)$, the ring of $2imes 2$ matrices over $C$, or $m=0$ and there exists $binQ_r$ such that$F(x)=bx$, for any $xin R$, with $ab=0$.

【 授权许可】

Unknown