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Semiderivations with Power Values on Lie Ideals in Prime Rings

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Ukrainian Mathematical Journal Aims and scope

Let R be a prime ring, let L a noncentral Lie ideal, and let f be a nonzero semiderivation associated with an automorphism σ such that f(u)n = 0 for all u ∈ L; where n is a fixed positive integer. If either Char R > n + 1 or Char R = 0; then R satisfies s 4; the standard identity in four variables.

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References

  1. K. I. Beidar, W. S. Martindale, and V. Mikhalev, “Rings with generalized identities,” Monogr. and Textbooks Pure Appl. Math., Marcel Dekker, Inc., New York, 196 (1996).

  2. J. Bergen, “Derivations in prime ring,” Can. Math. Bull., 26, No. 3, 267–270 (1983).

    Article  MathSciNet  MATH  Google Scholar 

  3. J. Bergen and L. Carini, “A note on derivations with power values on a Lie ideal,” Pacif. J. Math., 132, 209–213 (1988).

    Article  MathSciNet  MATH  Google Scholar 

  4. M. Brešar, “Semiderivations of prime rings,” Proc. Amer. Math. Soc., 108, No. 4, 859–860 (1990).

    MathSciNet  MATH  Google Scholar 

  5. J. C. Chang, “Generalized skew derivations with nilpotent values on Lie ideals,” Monatsh. Math., 161, 155–160 (2010).

    Article  MathSciNet  MATH  Google Scholar 

  6. C. L. Chuang, “GPIs having coefficients in Utumi quotient rings,” Proc. Amer. Math. Soc., 103, No. 3, 723–728 (1988).

    Article  MathSciNet  MATH  Google Scholar 

  7. C. L. Chuang, “Differential identities with automorphisms and anti-automorphisms,” J. Algebra, 160, 130–171 (1993).

    Article  MathSciNet  MATH  Google Scholar 

  8. L. Carini and A. Giambruno, “Lie ideals and nil derivations,” Boll. Unione Mat. Ital., 6, 497–503 (1985).

    MathSciNet  Google Scholar 

  9. J. S. Erickson, W. S. Martindale III, and J. M. Osborn, “Prime nonassociative algebras,” Pacif. J. Math., 60, No. 1, 49–63 (1975).

    Article  MathSciNet  MATH  Google Scholar 

  10. I. N. Herstein, “Center-like elements in prime rings,” J. Algebra, 60, 567–574 (1979).

    Article  MathSciNet  MATH  Google Scholar 

  11. N. Jacobson, Structure of Rings, Amer. Math. Soc., Provindence, RI (1964).

    Google Scholar 

  12. V. K. Kharchenko, “Generalized identities with automorphisms,” Algebra Logika, 14, 132–148 (1975).

    Article  Google Scholar 

  13. C. Lanski, “Derivations with nilpotent values on Lie ideals,” Proc. Amer. Math. Soc., 108, No. 1, 31–37 (1990).

    Article  MathSciNet  MATH  Google Scholar 

  14. T. K. Lee, “Generalized derivations of left faithful rings,” Comm. Algebra, 27, No. 8, 4057–4073 (1999).

    Article  MathSciNet  MATH  Google Scholar 

  15. W. S. Martindale III, “Prime rings satisfying a generalized polynomial identity,” J. Algebra, 12, 176–584 (1969).

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Chuzhou University, Chuzhou, China

    Shuliang Huang

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  1. Shuliang Huang
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 65, No. 6, pp. 870–873, June, 2013.

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Huang, S. Semiderivations with Power Values on Lie Ideals in Prime Rings. Ukr Math J 65, 967–971 (2013). https://doi.org/10.1007/s11253-013-0834-2

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  • DOI: https://doi.org/10.1007/s11253-013-0834-2

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