Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

JORDAN HIGHER DERIVATIONS ON TRIVIAL EXTENSION ALGEBRAS

  • Vishki, Hamid Reza Ebrahimi (Department of Pure Mathematics and Center of Excellence in Analysis on Algebraic Structures (CEAAS) Ferdowsi University of Mashhad) ;
  • Mirzavaziri, Madjid (Department of Pure Mathematics and Center of Excellence in Analysis on Algebraic Structures (CEAAS) Ferdowsi University of Mashhad) ;
  • Moafian, Fahimeh (Department of Pure Mathematics Ferdowsi University of Mashhad)
  • Received : 2015.07.01
  • Published : 2016.04.30
Download PDF
⟨ Previous Next ⟩

Abstract

We first give the constructions of (Jordan) higher derivations on a trivial extension algebra and then we provide some sufficient conditions under which a Jordan higher derivation on a trivial extension algebra is a higher derivation. We then proceed to the trivial generalized matrix algebras as a special trivial extension algebra. As an application we characterize the construction of Jordan higher derivations on a triangular algebra. We also provide some illuminating examples of Jordan higher derivations on certain trivial extension algebras which are not higher derivations.

Keywords

References

  1. D. Benkovic and N. sirovnik, Jordan derivations of unital algebras with idempotents, Linear Algebra Appl. 437 (2012), no. 9, 2271-2284. https://doi.org/10.1016/j.laa.2012.06.009
  2. M. Bresar, Jordan mappings of semiprime rings, J. Algebra 127 (1989), no. 1, 218-228. https://doi.org/10.1016/0021-8693(89)90285-8
  3. W.-S. Cheung, Mappings on triangular algebras, Ph.D Thesis, University of Victoria, 2000.
  4. H. Ghahramani, Jordan derivations on trivial extensions, Bull. Iranian Math. Soc. 39 (2013), no. 4, 635-645.
  5. I. N. Herstein, Jordan derivations of prime rings, Proc. Amer. Math. Soc. 8 (1957), 1104-1110. https://doi.org/10.1090/S0002-9939-1957-0095864-2
  6. Y. Li, L. van Wyk and F. Wei, Jordan derivations and antiderivations of generalized matrix algebras, Oper. Matrices 7 (2013), no. 2, 399-415.
  7. M. Mirzavaziri, Characterization of higher derivations on algebras, Comm. Algebra 38 (2010), no. 3, 981-987. https://doi.org/10.1080/00927870902828751
  8. F. Moafian, Higher derivations on trivial extension algebras and triangular algebras, Ph.D Thesis, Ferdowsi University of Mashhad, 2015.
  9. F. Moafian and H. R. Ebrahimi Vishki, Lie higher derivations on triangular algebras revisited, to appear in Filomat.
  10. A. H. Mokhtari, F. Moafian and H. R. Ebrahimi Vishki, Lie derivations on trivial extension algebras, arXiv:1504.05924v1 [math.RA].
  11. Y. Ohnuki, K. Takeda and K. Yamagata, Symmetric Hochschild extension algebras, Colloq. Math. 80 (1999), no. 2, 155-174. https://doi.org/10.4064/cm-80-2-155-174
  12. A. D. Sands, Radicals and Morita contexts, J. Algebra 24 (1973), 335-345. https://doi.org/10.1016/0021-8693(73)90143-9
  13. Z. Xiao and F. Wei, Jordan higher derivations on triangular algebras, Linear Algebra Appl. 432 (2010), no. 10, 2615-2622. https://doi.org/10.1016/j.laa.2009.12.006
  14. Z. Xiao and F. Wei, Jordan higher derivations on some operator algebras, Houston J. Math. 38 (2012), no. 1, 275-293.
  15. J. H. Zhang and W. Y. Yu, Jordan derivations of triangular algebras, Linear Algebra Appl. 419 (2006), no. 1, 251-255. https://doi.org/10.1016/j.laa.2006.04.015
  16. Y. Zhang, Weak amenability of module extensions of Banach algebras, Trans. Amer. Math. Soc. 354 (2002), no. 10, 4131-4151. https://doi.org/10.1090/S0002-9947-02-03039-8

Cited by

  1. Lie Derivations on Trivial Extension Algebras vol.31, pp.1, 2017, https://doi.org/10.1515/amsil-2016-0017
  2. Lie generalized derivations on trivial extension algebras pp.2198-2759, 2019, https://doi.org/10.1007/s40574-018-0177-x