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Fu, Wen-Lian, Xiao, Zhan-kui (2015)
Nonlinear Jordan Higher Derivations of Triangular Algebras, 31
Zhankui Xiao, F. Wei (2012)
Jordan higher derivations on some operator algebrasHouston Journal of Mathematics, 38
W. Cheung (2001)
Commuting Maps of Triangular AlgebrasJournal of the London Mathematical Society, 63
Peisheng Ji, W. Qi (2011)
Characterizations of Lie derivations of triangular algebrasLinear Algebra and its Applications, 435
A. Jabeen (2017)
Nonlinear Functions on Some Special Classes of Algebras
Jiankui Li, Q. Shen (2012)
CHARACTERIZATIONS OF LIE HIGHER AND LIE TRIPLE DERIVATIONS ON TRIANGULAR ALGEBRASJournal of Korean Medical Science, 49
Peisheng Ji, R. Liu, Yingzi Zhao (2012)
Nonlinear Lie triple derivations of triangular algebrasLinear and Multilinear Algebra, 60
M. Ashraf, A. Jabeen (2018)
Nonlinear Lie triple higher derivation on triangular algebras
X. Qi (2013)
Characterization of Lie higher derivations on triangular algebrasActa Mathematica Sinica, English Series, 29
Z Xiao, F Wei (2010)
Jordan higher derivations on triangular algebrasLinear Algebra Appl., 432
Zhankui Xiao, F. Wei (2012)
Nonlinear Lie higher derivations on triangular algebrasLinear and Multilinear Algebra, 60
M. Ferrero, C. Haetinger (2002)
Higher Derivations and a Theorem By HersteinQuaestiones Mathematicae, 25
M. Ashraf, A. Jabeen (2017)
Nonlinear generalized Lie triple derivation on triangular algebrasCommunications in Algebra, 45
D. Han (2014)
LIE-TYPE HIGHER DERIVATIONS ON OPERATOR ALGEBRAS
Qi, XIAO-FEIi, Hou, Jin-chuan (2010)
Lie Higher Derivations on Nest Algebras, 26
F. Wei, Zhankui Xiao (2011)
Higher derivations of triangular algebras and its generalizationsLinear Algebra and its Applications, 435
S. Chase (1961)
A Generalization of the Ring of Triangular MatricesNagoya Mathematical Journal, 18
WS Cheung (2003)
Lie derivation of triangular algebrasLinear Multilinear Algebra, 51
J Li, Q Shen (2012)
Characterizations of Lie higher and Lie triple derivations on triangular algebrasJ. Korean Math. Soc., 49
Aili Yang (2015)
Jordan Higher Derivations of Triangular AlgebrasInternational journal of applied mathematics and statistics, 53
Let $${\mathcal {R}}$$ R be a commutative ring with unity. A triangular algebra is an algebra of the form $${\mathfrak {A}} = \left[ \begin{array}{cc} {\mathcal {A}} &{} {\mathcal {M}} \\ 0 &{} {\mathcal {B}} \\ \end{array} \right] $$ A = A M 0 B where $${\mathcal {A}}$$ A and $${\mathcal {B}}$$ B are unital algebras over $${\mathcal {R}}$$ R and $${\mathcal {M}}$$ M is an $$({\mathcal {A}},{\mathcal {B}})$$ ( A , B ) -bimodule which is faithful as a left $${\mathcal {A}}$$ A -module as well as a right $${\mathcal {B}}$$ B -module. In this paper, we study nonlinear generalized Lie triple higher derivation on $${\mathfrak {A}}$$ A and show that under certain assumptions on $${\mathfrak {A}}$$ A , every nonlinear generalized Lie triple higher derivation on $${\mathfrak {A}}$$ A is of standard form, i.e., each component of a nonlinear generalized Lie triple higher derivation on $${\mathfrak {A}}$$ A can be expressed as the sum of an additive generalized higher derivation and a nonlinear functional vanishing on all Lie triple products on $${\mathfrak {A}}$$ A .
Bulletin of the Iranian Mathematical Society – Springer Journals
Published: Jun 4, 2018
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