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    • Annihilating Power Values of Co-Commutators with Generalized Derivations

      Basudeb Dhara

      Volume 122 Issue 1 February 2012 pp 121-128

    • Fulltext

       

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      Permanent link:
      https://www.ias.ac.in/article/fulltext/pmsc/122/01/0121-0128

    • Keywords

       

      Prime ring; derivation; generalized derivation; extended centroid; Utumi quotient ring.

    • Abstract

       

      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 $0\neq a\in R$ such that $a(H(u)u-uG(u))^n=0$ for all $u\in L$, where $n\geq 1$ is a fixed integer. Then there exist $b',c' \in U$ such that $H(x)=b'x+xc',G(x)=c'x$ for all $x\in R$ with $ab'=0$, unless 𝑅 satisfies $s4$, the standard identity in four variables.

    • Author Affiliations

       

      Basudeb Dhara1

      1. Department of Mathematics, Belda College, Belda, Paschim Medinipur 721 424, India

    • Dates

       
      Published
      February 2012
      Manuscript received
      30 November 2010

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