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On $ m$-commuting mappings with skew derivations in prime rings


Authors: N. Rehman and M. Arif Raza
Original publication: Algebra i Analiz, tom 27 (2015), nomer 4.
Journal: St. Petersburg Math. J. 27 (2016), 641-650
MSC (2010): Primary 16N60
DOI: https://doi.org/10.1090/spmj/1411
Published electronically: June 2, 2016
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Abstract | References | Similar Articles | Additional Information

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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Additional Information

N. Rehman
Affiliation: Department of Mathematics, Aligarh Muslim University, Aligarh-202002, India
Email: nu.rehman.mm@amu.ac.in

M. Arif Raza
Affiliation: Department of Mathematics, Aligarh Muslim University, Aligarh-202002, India
Email: arifraza03@gmail.com

DOI: https://doi.org/10.1090/spmj/1411
Keywords: Skew derivations, automorphism, generalized polynomial identity (GPI), prime ring, Lie ideal
Received by editor(s): March 2, 2015
Published electronically: June 2, 2016
Article copyright: © Copyright 2016 American Mathematical Society

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