Subsets with Generalized Derivations Having Nilpotent Values on Lie Ideals |
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| Authors: | Vincenzo De Filippis Giovanni Scudo |
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| Institution: | 1. Department of Mathematics and Computer Science, University of Messina, Italydefilippis@unime.it;3. Department of Mathematics and Computer Science, University of Messina, Italy |
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| Abstract: | Let R be a prime ring, with no nonzero nil right ideal, Q the two-sided Martindale quotient ring of R, F a generalized derivation of R, L a noncommutative Lie ideal of R, and b ∈ Q. If, for any u, w ∈ L, there exists n = n(u, w) ≥1 such that (F(uw) ? bwu)n = 0, then one of the following statements holds: F = 0 and b = 0; R ? M2(K), the ring of 2 × 2 matrices over a field K, b2 = 0, and F(x) = ?bx, for all x ∈ R.
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| Keywords: | Generalized derivation Prime ring |
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