Nonlinear Jordan Triple Derivations of Triangular Algebras

Abstract

In this paper, it is proved that every nonlinear Jordan triple derivation on triangular algebra is an additive derivation.

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Li, H. (2014) Nonlinear Jordan Triple Derivations of Triangular Algebras. Advances in Linear Algebra & Matrix Theory, 4, 205-209. doi: 10.4236/alamt.2014.44018.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] Bresar, M. (1989) Jordan Mappings of Semiprime Rings. Journal of Algebra, 127, 218-228.
http://dx.doi.org/10.1016/0021-8693(89)90285-8
[2] Herstein, I.N. (1969) Topics in Ring Theory. University of Chicago Press, Chicago, London.
[3] Wei, F. and Xiao, Z.K. (2009) Generalized Jordan Triple Higher Derivations on Semiprime Rings. Bulletin of the Korean Mathematical Society, 46, 553-565. http://dx.doi.org/10.4134/BKMS.2009.46.3.553
[4] Li, J.K. and Lu, F.Y. (2007) Additive Jordan Derivations of Reflexive Algebras. Journal of Mathematical Analysis and Applications, 329, 102-111. http://dx.doi.org/10.1016/j.jmaa.2006.06.019
[5] Zhang, J.H. (1998) Jordan Derivations on Nest Algebras. Acta Mathematica Sinica, Chinese Series, 41, 205-213. (In Chinese)
[6] Fosner, M. and Ilisevic, D. (2008) On Jordan Triple Derivations and Related Mappings. Mediterranean Journal of Mathematics, 5, 1660-5454. http://dx.doi.org/10.1007/s00009-008-0159-9
[7] Jing, W. and Lu, S. (2003) Generalized Jordan Derivations on Prime Rings and Standard Operator Algebras. Taiwanese Journal of Mathematics, 7, 605-613.
[8] Shang, Y. (2013) On the Ideals of Commutative Local Rings. Kochi Journal of Mathematics, 8, 13-17.
[9] Shang, Y. (2011) A Study of Derivations in Prime Near-Rings. Mathematica Balkanica (N.S.), 25, 413-418.
[10] Cheung, W.S. (2000) Mappings on Triangular Algebras. Ph.D. Dissertation, University of Victoria, British Columbia, Canada.
[11] Zhang, J.H. and Yu, W.Y. (2006) Jordan Derivations of Triangular Algebras. Linear Algebra and Its Applications, 419, 251-255. http://dx.doi.org/10.1016/j.laa.2006.04.015

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