Skip to main content
Log in

Characterizing Jordan Maps on Triangular Rings Through Commutative Zero Products

  • Published:
Mediterranean Journal of Mathematics Aims and scope Submit manuscript

Abstract

In this article, the structure of Jordan centralizers and Jordan generalized derivations on 2-torsion-free triangular rings through commutative zero products are given. By applying this results, we obtain some corollaries concerning (Jordan) centralizers and (Jordan) derivations on triangular rings.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Benkovič, D.: Jordan derivations and antiderivations on triangular matrices. Linear Algebra Appl. 397, 235–244 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  2. Benkovič, D., Eremita, D., Vukman, J.: A characterization of the centroid of a prime ring. Stud. Sci. Math. Hung. 45, 379–394 (2008)

    MathSciNet  MATH  Google Scholar 

  3. Brešar, M.: Jordan derivation on semiprime rings. Proc. Am. Math. Soc. 104, 1003–1006 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  4. Ghahramani, H.: Additive mappings derivable at nontrivial idempotents on Banach algebras. Linear Multilinear Algebra 60, 725–742 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  5. Ghahramani, H.: Zero product determined triangular algebras. Linear Multilinear Algebra 61, 741–757 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  6. Ghahramani, H.: Jordan derivations on trivial extensions. Bull. Iran. Math. Soc. 39, 635–645 (2013)

    MathSciNet  MATH  Google Scholar 

  7. Ghahramani, H.: Characterizing Jordan derivations of matrix rings through zero products. Math. Slovaca 65, 1277–1290 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  8. Ghahramani, H.: On centralizers of Banach algebras. Bull. Malays. Math. Sci. Soc. 38, 155–164 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  9. Guo, J., Li, J.: On centralizers of reflexive algebras. Aequ. Math. 84, 1–12 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  10. Herstein, I.N.: Jordan derivations on prime rings. Proc. Am. Math. Soc. 8, 1104–1110 (1957)

    Article  MathSciNet  MATH  Google Scholar 

  11. Jacobson, N., Rickart, C.E.: Jordan homomorphisms of rings. Trans. Am. Math. Soc. 69(3), 479–502 (1950)

    Article  MathSciNet  MATH  Google Scholar 

  12. Li, Y., Benkovič, D.: Jordan generalized derivations on triangular algebras. Linear Multilinear Algebra 59, 841–849 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  13. Vukman, J.: An identity related to centralizers in semiprime rings. Comment. Math. Univ. Carol. 40, 447–456 (1999)

    MathSciNet  MATH  Google Scholar 

  14. Vukman, J.: Centralizers on semiprime rings. Comment. Math. Univ. Carol. 42, 237–245 (2001)

    MathSciNet  MATH  Google Scholar 

  15. Zhang, J.H., Yu, W.Y.: Jordan derivations of triangular algebras. Linear Algebra Appl. 419, 251–255 (2006)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Hoger Ghahramani.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ghahramani, H. Characterizing Jordan Maps on Triangular Rings Through Commutative Zero Products. Mediterr. J. Math. 15, 38 (2018). https://doi.org/10.1007/s00009-018-1082-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00009-018-1082-3

Mathematics Subject Classification

Keywords

Navigation