Skip to main content
SpringerLink
Log in

On Commutativity of Rings With Derivations

  • Published:
Results in Mathematics Aims and scope Submit manuscript

Abstract

Let R be a ring and d : R → R a derivation of R. In the present paper we investigate commutativity of R satisfying any one of the properties (i)d([x,y]) = [x,y], (ii)d(x o y) = xoy, (iii)d(x) o d(y) = 0, or (iv)d(x) o d(y) = x o y, for all x, y in some apropriate subset of R.

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. Awtar, R., Lie structure in prime rings with derivations, Publ. Math.(Debrecen) 31 (1984), 209–215.

    MathSciNet  MATH  Google Scholar 

  2. Awtar, R., Lie and Jordan structures in prime rings with derivations, Proc. Amer. Math. Soc. 41 (1973), 67–74.

    Article  MathSciNet  MATH  Google Scholar 

  3. Bell, H.E. and Daif, M.N., On commutativity and strong commutativity preserving maps, Canad. Math. Bull. 37 (1994), 443–447.

    Article  MathSciNet  MATH  Google Scholar 

  4. Bell, H. E. and Martindale, W. S., Centralizing mappings of semiprime rings, Canad.Math. Bull. 30 (1987), 92–101.

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  6. Bresar, M., Commuting traces of biadditive mappings, commutativity preserving mappings and Lie mappings, Trans.Amer. Math. Soc. 335 (1993), 525–546.

    MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  8. Daif, M. N. and Bell, H. E., Remarks on derivations on semiprime rings, Internal. J. Math, &: Math. Sci. 15 (1992), 205–206.

    Article  MathSciNet  MATH  Google Scholar 

  9. Deng, Q. and Ashraf, M., On strong commutativity preserving mappings, Results in Math. 30 (1996), 259–263.

    Article  MathSciNet  MATH  Google Scholar 

  10. Herstein, I. N., Ring with involution, Univ. Chicago press, Chicago 1976.

    Google Scholar 

  11. Herstein, I. N., Topics in ring theory, Univ. Chicago press, Chicago 1969.

    MATH  Google Scholar 

  12. Hongan, M., A note on semiprime rings with derivations, Internat. J. Math. & Math. Sci. 20 (1997), 413–415.

    Article  MathSciNet  MATH  Google Scholar 

  13. Mayne, J.H., Centralizing mappings of prime rings, Canad. Math. Bull. 27 (1984), 122–126.

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics Faculty of science, King Abdul Aziz University, P.O. Box. 80203, Jeddah, 21589, Saudi-Arabia

    Mohammad Ashraf

  2. Department of Mathematics, Aligarh Muslim University, Aligarh, India

    Nadeem-ur Rehman

Authors
  1. Mohammad Ashraf
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Nadeem-ur Rehman
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ashraf, M., Rehman, Nu. On Commutativity of Rings With Derivations. Results. Math. 42, 3–8 (2002). https://doi.org/10.1007/BF03323547

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF03323547

Keywords and Phrases

1991 Mathematics Subject Classification

Search

Navigation