Power Cocentralizing Generalized Derivations on Prime Rings

Proceedings Mathematical Sciences

Vincenzo De Filippis¹ 

[1] DI.S.I.A., Faculty of Engineering, University of Messina, Messina, Italy$$

关键词: Prime rings;    differential identities;    generalized derivations.;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

Let 𝑅 be a prime ring, 𝑈 the Utumi quotient ring of $R,C=Z(U)$ the extended centroid of 𝑅,𝐿 a non-central Lie ideal of 𝑅,𝐻 and 𝐺 non-zero generalized derivations of 𝑅. Suppose that there exists an integer $n≥ 1$ such that $(H(u)u-uG(u))^n=0$, for all $uin L$, then one of the following holds: (1) there exists $cin U$ such that $H(x)=xc,G(x)=cx;(2)R$ satisfies the standard identity $s_4$ and char (𝑅)=2; (3) 𝑅 satisfies $s4$ and there exist $a, b, cin U$, such that $H(x)=ax+xc,G(x)=cx+xb$ and $(a-b)^n=0$.

【 授权许可】

Unknown