Taiwanese Journal of Mathematics


Nurc¸an Argac, Luisa Carini, and Vincenzo De Filippis

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Let $R$ be a prime ring, with extended centroid $C$, $g$ a non-zero generalized derivation of $R$, $L$ a non-central Lie ideal of $R$, $k\geq 1$ a fixed integer. If $[g(u),u]_k=0$, for all $u$, then either $g(x)=ax$, with $a \in C$ or $R$ satisfies the standard identity $s_4$. Moreover in the latter case either $char(R)=2$ or $char(R)\neq 2$ and $g(x)=ax+xb$ , with $a,b \in Q$ and $a-b\in C$. We also prove a more generalized version by replacing $L$ with the set $[I,I]$, where $I$ is a right ideal of $R$.

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Taiwanese J. Math., Volume 12, Number 2 (2008), 419-433.

First available in Project Euclid: 20 July 2017

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Zentralblatt MATH identifier

Primary: 16N60: Prime and semiprime rings [See also 16D60, 16U10] 16W25: Derivations, actions of Lie algebras

generalized derivation differential identity generalized polynomial identity


Argac, Nurc¸an; Carini, Luisa; Filippis, Vincenzo De. AN ENGEL CONDITION WITH GENERALIZED DERIVATIONS ON LIE IDEALS. Taiwanese J. Math. 12 (2008), no. 2, 419--433. doi:10.11650/twjm/1500574164. https://projecteuclid.org/euclid.twjm/1500574164

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