Skip to main content
SpringerLink
Log in

Biderivations of Triangular Rings Revisited

  • Published:
Bulletin of the Malaysian Mathematical Sciences Society Aims and scope Submit manuscript

Abstract

We consider the problem of describing the form of biderivations of a triangular ring. Our approach is based on the notion of the maximal left ring of quotients, which enables us to generalize Benkovič’s result on biderivations (Benkovič in Linear Algebra Appl 431:1587–1602, 2009). Our result is applied to block upper triangular matrix rings and nest algebras.

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. Aranda Pino, G., Gómez Lozano, M.A., Siles Molina, M.: Morita invariance and maximal left quotient rings. Commun. Algebra 32(8), 3247–3256 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  2. Benkovič, D.: Biderivations of triangular algebras. Linear Algebra Appl. 431, 1587–1602 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  3. Brešar, M.: On generalized biderivations and related maps. J. Algebra 172, 764–786 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  4. Brešar, M.: Commuting maps: a survey. Taiwan. J. Math. 8(3), 361–397 (2004)

    MathSciNet  MATH  Google Scholar 

  5. Brešar, M., Martindale 3rd, W.S., Miers, C.R.: Centralizing maps in prime rings with involution. J. Algebra 161, 342–357 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  6. Cheung, W.-S.: Commuting maps of triangular algebras. J. Lond. Math. Soc. 63(2), 117–127 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  7. Davidson, K.R.: Nest Algebras. Pitman Research Notes in Mathematics Series 191. Longmans, Harlow (1988)

    MATH  Google Scholar 

  8. Eremita, D.: Functional identities of degree 2 in triangular rings revisited. Linear Multilinear Algebra 63(3), 534–553 (2015)

  9. Ghosseiri, N.M.: On biderivations of upper triangular matrix rings. Linear Algebra Appl. 438(1), 250–260 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  10. Lam, T.Y.: Lectures on Modules and Rings. Graduate Texts in Mathematics, 189. Springer, New York (1999)

    Book  MATH  Google Scholar 

  11. Passman, D.S.: A Course in Ring Theory. Wadsworth & Brooks/Cole Advanced Books & Software, Pacific Grove, CA (1991)

    MATH  Google Scholar 

  12. Zhang, J.-H., Feng, S., Li, H.-X., Wu, R.-H.: Generalized biderivations of nest algebras. Linear Algebra Appl. 418, 225–233 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  13. Zhao, Y., Wang, D., Yao, R.: Biderivations of upper triangular matrix algebras over commutative rings. Int. J. Math. Game Theory Algebra 18(6), 473–478 (2009)

    MathSciNet  MATH  Google Scholar 

  14. Utumi, Y.: On quotient rings. Osaka J. Math. 8, 1–18 (1956)

    MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

The author is thankful to his colleague Professor Dominik Benkovič for some useful suggestions regarding Sect.  4.

Author information

Authors and Affiliations

  1. Department of Mathematics and Computer Science, FNM, University of Maribor, 2000, Maribor, Slovenia

    Daniel Eremita

Authors
  1. Daniel Eremita
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Daniel Eremita.

Additional information

Communicated by Kar Ping Shum.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Eremita, D. Biderivations of Triangular Rings Revisited. Bull. Malays. Math. Sci. Soc. 40, 505–522 (2017). https://doi.org/10.1007/s40840-017-0451-6

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40840-017-0451-6

Keywords

Mathematics Subject Classification

Search

Navigation