Skip to main content
SpringerLink
Log in

Annihilator condition on power values of derivations

  • Published:
Indian Journal of Pure and Applied Mathematics Aims and scope Submit manuscript

Abstract

Let R be a prime ring, d, δ two derivations of R, L a noncentral Lie ideal of R and 0 ≠ a ∈ R. The main object in this paper is to discuss the situations a (d (x)x − xδ (x))n = 0 for all x ∈ L and a (d (x)x − xδ (x)) ∈ Z (R) for all x ∈ L, where n ≥ 1 is a fixed integer.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. N. Argac and V. De Filippis, Co-centralizing derivations and nilpotent values on Lie ideals, Indian J. Pure Appl. Math., 41(3) (2010), 475–483.

    Article  MATH  MathSciNet  Google Scholar 

  2. K. I. Beidar, W. S. Martindale III and A. V. Mikhalev, Rings with generalized identities, Pure and Applied Math., 196, Marcel Dekker, New York, 1996.

    MATH  Google Scholar 

  3. J. Bergen, I. N. Herstein and J.W. Kerr, Lie ideals and derivations of prime rings, J. Algebra, 71 (1981), 259–267.

    Article  MATH  MathSciNet  Google Scholar 

  4. M. Brešar, Centralizing mappings and derivations in prime rings, J. Algebra 156 (1993), 385–394.

    Article  MATH  MathSciNet  Google Scholar 

  5. L. Carini and V. De Filippis, Commutators with power central values on a Lie ideal, Pacific J. Math., 193(2) (2000), 269–278.

    Article  MATH  MathSciNet  Google Scholar 

  6. C. M. Chang and T. K. Lee, Annihilators of power values of derivations in prime rings, Comm. Algebra, 26(7) (1998), 2091–2113.

    Article  MATH  MathSciNet  Google Scholar 

  7. C. L. Chuang, GPI’s having coefficients in Utumi quotient rings, Proc. Amer. Math. Soc., 103(3) (1988), 723–728.

    Article  MATH  MathSciNet  Google Scholar 

  8. B. Dhara, Power values of derivations with annihilator conditions on Lie ideals in prime rings, Comm. Algebra, 37(6) (2009), 2159–2167.

    Article  MATH  MathSciNet  Google Scholar 

  9. T. S. Erickson, W. S. Martindale III and J. M. Osborn, Prime nonassociative algebras, Pacific J. Math., 60 (1975), 49–63.

    MATH  MathSciNet  Google Scholar 

  10. V. De Filippis, Lie ideals and annihilator conditions on power values of commutators with derivation, Indian J. Pure Appl. Math., 32 (2001), 649–656.

    MATH  MathSciNet  Google Scholar 

  11. I. N. Herstein, Rings with involution, Univ. of Chicago Press, Chicago, 1976.

    MATH  Google Scholar 

  12. I. N. Herstein, Topics in ring theory, Univ. of Chicago Press, Chicago, IL, 1969.

    MATH  Google Scholar 

  13. V. K. Kharchenko, Differential identity of prime rings, Algebra and Logic., 17 (1978), 155–168.

    Article  MATH  Google Scholar 

  14. C. Lanski and S. Montgomery, Lie structure of prime rings of characteristic 2, Pacific J. Math., 42(1) (1972), 117–136.

    MATH  MathSciNet  Google Scholar 

  15. C. Lanski, Differential identities, Lie ideals, and Posner’s theorems, Pacific J. Math., 134(2) (1988), 275–297.

    MATH  MathSciNet  Google Scholar 

  16. C. Lanski, An engel condition with derivation, Proc. Amer. Math. Soc., 118(3) (1993), 731–734.

    Article  MATH  MathSciNet  Google Scholar 

  17. T. K. Lee, Semiprime rings with differential identities, Bull. Inst. Math. Acad. Sinica, 20(1) (1992), 27–38.

    MATH  MathSciNet  Google Scholar 

  18. P. H. Lee, Lie ideals of prime rings with derivations, Bull. Inst. Math. Acad. Sinica, 11 (1983), 75–80.

    MATH  MathSciNet  Google Scholar 

  19. P. H. Lee and T. L. Wong, Derivations cocentralizing Lie ideals, Bull. Inst. Math. Acad. Sinica, 23 (1995), 1–5.

    MATH  MathSciNet  Google Scholar 

  20. W. S. Martindale III, Prime rings satisfying a generalized polynomial identity, J. Algebra, 12 (1969), 576–584.

    Article  MATH  MathSciNet  Google Scholar 

  21. E. C. Posner, Derivations in prime rings, Proc. Amer. Math. Soc., 8 (1957), 1093–1100.

    Article  MathSciNet  Google Scholar 

  22. Y. Wang, Annihilator conditions with derivations in prime rings of characteristic 2, Indian J. Pure Appl. Math., 39(6) (2008), 459–465.

    MATH  MathSciNet  Google Scholar 

  23. Y. Wang and H. You, A note on commutators with power central values on Lie ideals, Acta Math. Sinica, English Series, 22(6) (2006), 1715–1720.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Belda College, Belda Paschim Medinipur, 721424, India

    Basudeb Dhara

Authors
  1. Basudeb Dhara
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Basudeb Dhara.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dhara, B. Annihilator condition on power values of derivations. Indian J Pure Appl Math 42, 357–369 (2011). https://doi.org/10.1007/s13226-011-0023-7

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13226-011-0023-7

Key words

Search

Navigation