A note on generalized Lie derivations of prime rings
Articles > Article · 2016
Authors: Nihan BAYDAR YARBİL, Nurcan ARGAÇ
FRONTIERS OF MATHEMATICS IN CHINA, Journal Indexed in SCI Expanded, International, 2016, vol 12, pp 247-260
DOI: 10.1007/s11464-016-0589-9
Summary
Let R be a prime ring of characteristic not 2, A be an additive subgroup of R, and F, T, D, K: A-R be additive maps such that F([x, y]) = F(x) (y-y) K(x)-T(y) (x + x) D(y) for all x, y E 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.