On 𝑚-commuting mappings with skew derivations in prime rings

Rehman, N.; Raza, M.

doi:10.1090/spmj/1411

On $m$-commuting mappings with skew derivations in prime rings
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by N. Rehman and M. Arif Raza

St. Petersburg Math. J. 27 (2016), 641-650

DOI: https://doi.org/10.1090/spmj/1411

Published electronically: June 2, 2016

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Abstract:

Let $m,k$ be two fixed positive integers, $R$ a prime ring with the Martindale qoutient ring $Q$, $L$ a noncommutative Lie ideal of $R$, and $\delta$ a skew derivation of $R$ associated with an automorphism $\varphi$, denoted by $(\delta ,\varphi )$. If $[\delta (x), x^m]_k=0$ for all $x\in L$, then $\mathrm {char}(R)=2$ and $R\subseteq M_2(F)$ for some field $F$.

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