Advertisement

Ukrainian Mathematical Journal

, Volume 65, Issue 6, pp 967–971 | Cite as

Semiderivations with Power Values on Lie Ideals in Prime Rings

  • Shuliang Huang
Article
  • 85 Downloads

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 uL; 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.

Keywords

Prime Ring Generalize Derivation Nonzero Ideal Semiprime Ring Standard Identity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 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).Google Scholar
  2. 2.
    J. Bergen, “Derivations in prime ring,” Can. Math. Bull., 26, No. 3, 267–270 (1983).MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    J. Bergen and L. Carini, “A note on derivations with power values on a Lie ideal,” Pacif. J. Math., 132, 209–213 (1988).MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    M. Brešar, “Semiderivations of prime rings,” Proc. Amer. Math. Soc., 108, No. 4, 859–860 (1990).MathSciNetzbMATHGoogle Scholar
  5. 5.
    J. C. Chang, “Generalized skew derivations with nilpotent values on Lie ideals,” Monatsh. Math., 161, 155–160 (2010).MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    C. L. Chuang, “GPIs having coefficients in Utumi quotient rings,” Proc. Amer. Math. Soc., 103, No. 3, 723–728 (1988).MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    C. L. Chuang, “Differential identities with automorphisms and anti-automorphisms,” J. Algebra, 160, 130–171 (1993).MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    L. Carini and A. Giambruno, “Lie ideals and nil derivations,” Boll. Unione Mat. Ital., 6, 497–503 (1985).MathSciNetGoogle Scholar
  9. 9.
    J. S. Erickson, W. S. Martindale III, and J. M. Osborn, “Prime nonassociative algebras,” Pacif. J. Math., 60, No. 1, 49–63 (1975).MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    I. N. Herstein, “Center-like elements in prime rings,” J. Algebra, 60, 567–574 (1979).MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    N. Jacobson, Structure of Rings, Amer. Math. Soc., Provindence, RI (1964).Google Scholar
  12. 12.
    V. K. Kharchenko, “Generalized identities with automorphisms,” Algebra Logika, 14, 132–148 (1975).CrossRefGoogle Scholar
  13. 13.
    C. Lanski, “Derivations with nilpotent values on Lie ideals,” Proc. Amer. Math. Soc., 108, No. 1, 31–37 (1990).MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    T. K. Lee, “Generalized derivations of left faithful rings,” Comm. Algebra, 27, No. 8, 4057–4073 (1999).MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    W. S. Martindale III, “Prime rings satisfying a generalized polynomial identity,” J. Algebra, 12, 176–584 (1969).MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Shuliang Huang
    • 1
  1. 1.Chuzhou UniversityChuzhouChina

Personalised recommendations