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Cocentralizing derivations and nilpotent values on Lie ideals

Author

Listed:
  • Nurcan Argac

    (Ege University, Science Faculty)

  • Vincenzo Filippis

    (Faculty of Engineering University of Messina)

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).

Suggested Citation

  • Nurcan Argac & Vincenzo Filippis, 2010. "Cocentralizing derivations and nilpotent values on Lie ideals," Indian Journal of Pure and Applied Mathematics, Springer, vol. 41(3), pages 475-483, June.
    • Handle: RePEc:spr:indpam:v:41:y:2010:i:3:d:10.1007_s13226-010-0029-6
    DOI: 10.1007/s13226-010-0029-6
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    Cited by:

    1. Basudeb Dhara, 2011. "Annihilator condition on power values of derivations," Indian Journal of Pure and Applied Mathematics, Springer, vol. 42(5), pages 357-369, October.
    2. Basudeb Dhara & Nurcan Argaç & Krishna Gopal Pradhan, 2016. "Annihilator condition of a pair of derivations in prime and semiprime rings," Indian Journal of Pure and Applied Mathematics, Springer, vol. 47(1), pages 111-124, March.

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