Annihilating Power Values of Co-Commutators with Generalized Derivations

Proceedings Mathematical Sciences

Basudeb Dhara¹ 

[1] Department of Mathematics, Belda College, Belda, Paschim Medinipur , India$$

关键词: Prime ring;    derivation;    generalized derivation;    extended centroid;    Utumi quotient ring.;   

DOI  :  

学科分类：数学（综合）

来源: Indian Academy of Sciences

【 摘 要 】

Let 𝑅 be a prime ring with its Utumi ring of quotient 𝑈,𝐻 and 𝐺 be two generalized derivations of 𝑅 and 𝐿 a noncentral Lie ideal of 𝑅. Suppose that there exists $0≠ ain R$ such that $a(H(u)u-uG(u))^n=0$ for all $uin L$, where 𝑛 ≥ 1 is a fixed integer. Then there exist $b',c' in U$ such that $H(x)=b'x+xc',G(x)=c'x$ for all $xin R$ with $ab'=0$, unless 𝑅 satisfies 𝑠4, the standard identity in four variables.

【 授权许可】

Unknown