Siberian Mathematical Journal

, Volume 53, Issue 6, pp 1029–1036 | Cite as

Higher derivations on Lie ideals of triangular algebras



Let T be a triangular algebra and let U be an admissible Lie ideal of T. We mainly consider the question whether each Jordan higher derivation of U into T is a higher derivation of U into T. We also give some characterizations for the Jordan triple higher derivations of U.


admissible Lie ideal, triangular algebra higher derivation, Jordan (triple) higher derivation 


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  1. 1.
    Chase S. U., “A generalization of the ring of triangular matrices,” Nagoya Math. J., 18, 13–25 (1961).MathSciNetzbMATHGoogle Scholar
  2. 2.
    Harada M., “Hereditary semi-primary rings and tri-angular matrix rings,” Nagoya Math. J., 27, 463–484 (1966).MathSciNetzbMATHGoogle Scholar
  3. 3.
    Haghany A. and Varadarajan K., “Study of formal triangular matrix rings,” Comm. Algebra, 27, 5507–5525 (1999).MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Awtar R., “Lie ideals and Jordan derivations of prime rings,” Proc. Amer. Math. Soc., 90, No. 1, 9–14 (1984).MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Ferrero M. and Haetinger C., “Higher derivations and a theorem by Herstein,” Quaest. Math., 25, No. 2, 249–257 (2002).MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Ashraf M., Khan A., and Haetinger C., “On (σ, τ)-higher derivations in prime rings,” Int. Electron. J. Algebra, 8, 65–79 (2010).MathSciNetzbMATHGoogle Scholar
  7. 7.
    Cortes W. and Haetinger C., “On Jordan generalized higher derivations in rings,” Turkish J. Math., 29, No. 1, 1–10 (2005).MathSciNetzbMATHGoogle Scholar
  8. 8.
    Haetinger C., “Higher derivations on Lie ideals,” Tend. Mat. Apl. Comput., 3, No. 1, 141–145 (2002).MathSciNetzbMATHGoogle Scholar
  9. 9.
    Jung Y. S., “Generalized Jordan triple higher derivations on prime rings,” Indian J. Pure Appl. Math., 36, No. 9, 513–524 (2005).MathSciNetzbMATHGoogle Scholar
  10. 10.
    Nakajima A., “On generalized higher derivations,” Turkish J. Math., 24, No. 3, 485–487 (1992).MathSciNetGoogle Scholar
  11. 11.
    Wei F. and Xiao Z.H., “Jordan higher derivations on triangular algebras,” Linear Algebra Appl., 432, No. 10, 2615–2622 (2010).MathSciNetzbMATHCrossRefGoogle Scholar
  12. 12.
    Bergen J., Herstein I. N., and Kerr J. W., “Lie ideals and derivations of prime rings,” J. Algebra, 71, 259–267 (1981).MathSciNetzbMATHCrossRefGoogle Scholar
  13. 13.
    Lanski C. and Montgomery S., “Lie structure of prime rings of characteristic 2,” Pacific J. Math., 42, 117–136 (1972).MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2012

Authors and Affiliations

  1. 1.School of Mathematics and Information Science Henan Polytechnic UniversityJiaozuoP. R. China

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