RESEARCH ARTICLE

A note on generalized Lie derivations of prime rings

  • Nihan Baydar YARBIL ,
  • Nurcan ARGAC
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  • Department of Mathematics, Science Faculty, Ege University, 35100 Bornova, Izmir, Turkey

Received date: 20 Nov 2015

Accepted date: 03 May 2016

Published date: 01 Feb 2017

Copyright

2016 Higher Education Press and Springer-Verlag Berlin Heidelberg

Abstract

Let R be a prime ring of characteristic not 2, A be an additive subgroup of R, and F, T, D,K: AR be additive maps such that F[x, y]) = F(x)yyK(x) − T(y)x + xD(y) for all x, y ∈ A. Our aim is to deal with this functional identity when A is R itself or a noncentral Lie ideal of R. Eventually, we are able to describe the forms of the mappings F, T, D, and K in case A = R with deg(R)>3 and also in the case A is a noncentral Lie ideal and deg(R)>9. These enable us in return to characterize the forms of both generalized Lie derivations, D-Lie derivations and Lie centralizers of R under some mild assumptions. Finally, we give a generalization of Lie homomorphisms on Lie ideals.

Cite this article

Nihan Baydar YARBIL , Nurcan ARGAC . A note on generalized Lie derivations of prime rings[J]. Frontiers of Mathematics in China, 2017 , 12(1) : 247 -260 . DOI: 10.1007/s11464-016-0589-9

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