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A note on generalized Lie derivations of prime rings

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics, Science Faculty, Ege University, 35100, Bornova, Izmir, Turkey

    Nihan Baydar Yarbil & Nurcan Argaç

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  1. Nihan Baydar Yarbil
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  2. Nurcan Argaç
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Correspondence to Nihan Baydar Yarbil.

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Yarbil, N.B., Argaç, N. A note on generalized Lie derivations of prime rings. Front. Math. China 12, 247–260 (2017). https://doi.org/10.1007/s11464-016-0589-9

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  • DOI: https://doi.org/10.1007/s11464-016-0589-9

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