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Cocentralizing derivations and nilpotent values on Lie ideals

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Abstract

Let R be a prime ring with char R ≠ 2, L a non-central Lie ideal of R, d, g non-zero derivations of R, n ≥ 1 a fixed integer. We prove that if (d(x)x − xg(x))n = 0 for all x ∈ L, then either d = g = 0 or R satisfies the standard identity s 4 and d, g are inner derivations, induced respectively by the elements a and b such that a + b ∈ Z(R).

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Authors and Affiliations

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

    Nurcan Argac

  2. DI.S.I.A., Faculty of Engineering University of Messina, 98166, Messina, Italy

    Vincenzo De Filippis

Authors
  1. Nurcan Argac
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  2. Vincenzo De Filippis
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Correspondence to Nurcan Argac.

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Argac, N., De Filippis, V. Cocentralizing derivations and nilpotent values on Lie ideals. Indian J Pure Appl Math 41, 475–483 (2010). https://doi.org/10.1007/s13226-010-0029-6

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  • DOI: https://doi.org/10.1007/s13226-010-0029-6

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