Cocentralizing derivations and nilpotent values on Lie ideals

Nurcan Argac () and Vincenzo Filippis ()
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Nurcan Argac: Ege University, Science Faculty
Vincenzo Filippis: Faculty of Engineering University of Messina

Indian Journal of Pure and Applied Mathematics, 2010, vol. 41, issue 3, 475-483

Abstract: 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).

Keywords: Prime rings; Differential identities; Generalized derivations (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s13226-010-0029-6

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