• Annihilating Power Values of Co-Commutators with Generalized Derivations

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    • 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

  • Proceedings – Mathematical Sciences | News

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