Skip to main content
SpringerLink
Log in

A note on Jordan derivations of triangular rings

  • Published:
Aequationes mathematicae Aims and scope Submit manuscript

Abstract

In this note we prove that every Jordan derivation on a triangular ring is a derivation. Moreover, we show that, under some conditions, every Jordan derivation on a 2-torsion free ring is a derivation.

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

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  3. Brešar, M.: Jordan derivations revisited. Math. Proc. Camb. Philos. Soc. 139, 411–425 (2005)

    Article  MathSciNet  Google Scholar 

  4. Cheung, W.S.: Commuting maps on triangular algebras. J. Lond. Math. Soc. 63, 117–127 (2001)

    Article  MathSciNet  Google Scholar 

  5. Davidson, K.R.: Nest Algebras. Wiley, New York (1988)

    MATH  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  7. Jeon, Y.C., Kim, N.K., Lee, Y.: On fully idempotent rings. Bull. Korean Math. Soc. 47, 715–726 (2010)

    Article  MathSciNet  Google Scholar 

  8. Johnson, B.E.: Symmetric amenability and the nonexistence of Lie and Jordan derivations. Math. Proc. Camb. Philos. Soc. 120, 455–473 (1996)

    Article  MathSciNet  Google Scholar 

  9. Zhang, J., Yu, W.: Jordan derivations of triangular algberas. Linear Algebra Appl. 419, 251–255 (2006)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

This Project was supported by the Slovenian Research Agency (Project Number BI-US/18-19-017).

Author information

Authors and Affiliations

  1. Faculty of Management, University of Primorska, Koper, Slovenia

    Ajda Fošner

  2. Department of Mathematics and Computer Science, Fayetteville State University, Fayetteville, NC, 28301, USA

    Wu Jing

Authors
  1. Ajda Fošner
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Wu Jing
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ajda Fošner.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Fošner, A., Jing, W. A note on Jordan derivations of triangular rings. Aequat. Math. 94, 277–285 (2020). https://doi.org/10.1007/s00010-019-00689-y

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00010-019-00689-y

Keywords

Mathematics Subject Classification

Search

Navigation