Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Communications in Mathematics

Editor-in-Chief: Rossi, Olga

2 Issues per year


Mathematical Citation Quotient (MCQ) 2016: 0.28

Open Access
Online
ISSN
2336-1298
See all formats and pricing
More options …

Generalized Higher Derivations on Lie Ideals of Triangular Algebras

Mohammad Ashraf
  • Corresponding author
  • Mohammad Ashraf, Bilal Ahmad Wani, Department of Mathematics, Aligarh Muslim University, Aligarh, 202002, India
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Nazia Parveen / Bilal Ahmad Wani
Published Online: 2017-06-28 | DOI: https://doi.org/10.1515/cm-2017-0005

Abstract

Let be the triangular algebra consisting of unital algebras A and B over a commutative ring R with identity 1 and M be a unital (A; B)-bimodule. An additive subgroup L of A is said to be a Lie ideal of A if [L;A] ⊆ L. A non-central square closed Lie ideal L of A is known as an admissible Lie ideal. The main result of the present paper states that under certain restrictions on A, every generalized Jordan triple higher derivation of L into A is a generalized higher derivation of L into A.

Keywords: Admissible Lie Ideals; triangular algebra; generalized higher derivation; general- ized Jordan higher derivation; generalized Jordan triple higher derivation

References

  • [1] M. Ashraf, A. Khan, C. Haetinger: On (σ,τ)-higher derivations in prime rings. Int. Electron. J. Math. 8 (1) (2010) 65{79.Google Scholar

  • [2] M. Ashraf, A. Khan: On generalized (σ,τ)-higher derivations in prime rings. SpringerPlus 38 (2012).Web of ScienceGoogle Scholar

  • [3] R. Awtar: Lie ideals and Jordan derivations of prime rings. Proc. Amer. Math. Soc. 90 (1) (1984) 9{14.CrossrefGoogle Scholar

  • [4] J. Bergen, I. N. Herstein, J. W. Kerr: Lie ideals and derivations of prime rings. J. Algebra 71 (1981) 259{267.CrossrefGoogle Scholar

  • [5] M. Bre¹ar: On the distance of the composition of two derivations to the generalized derivations. Glasgow Math. J. 33 (1991) 89{93.Google Scholar

  • [6] S. U. Chase: A generalization of the ring of triangular matrices. Nagoya Math. J. 18 (1961) 13{25.Google Scholar

  • [7] W. Cortes, C. Haetinger: On Jordan generalized higher derivations in rings. Turkish J. Math. 29 (1) (2005) 1{10.Google Scholar

  • [8] M. Ferrero, C. Haetinger: Higher derivations and a theorem by Herstein. Quaest. Math. 25 (2) (2002) 249{257.CrossrefGoogle Scholar

  • [9] M. Ferrero, C. Haetinger: Higher derivations of semiprime rings. Comm. Algebra 30 (5) (2002) 2321{2333.CrossrefGoogle Scholar

  • [10] C. Haetinger: Higher derivation on Lie ideals. Tend. Mat. Apl. Comput. 3 (1) (2002) 141{145.CrossrefGoogle Scholar

  • [11] C. Haetinger, M. Ashraf, S. Ali: On Higher derivations: a survey. Int. J. Math. Game Theory Algebra 19 (5/6) (2011) 359{379.Google Scholar

  • [12] D. Han: Higher derivations on Lie ideals of triangular algebras. Sib. Math. J. 53 (6) (2012) 1029{1036.Web of ScienceCrossrefGoogle Scholar

  • [13] F. Hasse, F. K. Schmidt: Noch eine Begründung der Theorie der höheren DiKerentialquotienten einem algebraischen Funktionenköroer einer Unbestimmten. J. reine angew. Math. 177 (1937) 215{237.Google Scholar

  • [14] W. Jing, S. Lu: Generalized Jordan derivations on prime rings and standard operator algebras. Taiwanese J. Math. 7 (4) (2003) 605{613.Google Scholar

  • [15] Y. S. Jung: Generalized Jordan triple higher derivations on prime rings. Indian J. Pure Appl. Math. 36 (9) (2005) 513{524.Google Scholar

  • [16] C. Lanski, S. Montgomery: Lie structure of prime rings of characteristic 2. Paci_c J. Math. 42 (1972) 117{136.Google Scholar

  • [17] A. Nakajima: On generalized higher derivations. Turk. J. Math. 24 (3) (2000) 295{311.Google Scholar

  • [18] Z. H. Xiao, F. Wei: Jordan higher derivations on triangular algebras. Linear Algebra Appl. 432 (2010) 2615{2622.Web of ScienceGoogle Scholar

About the article

Received: 2016-12-08

Accepted: 2017-02-25

Published Online: 2017-06-28

Published in Print: 2017-06-27


Citation Information: Communications in Mathematics, ISSN (Online) 2336-1298, DOI: https://doi.org/10.1515/cm-2017-0005.

Export Citation

© 2017. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. BY-NC-ND 4.0

Comments (0)

Please log in or register to comment.
Log in