Nonlinear Generalized Lie Triple Higher Derivation on Triangular Algebras

Nonlinear Generalized Lie Triple Higher Derivation on Triangular Algebras 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 . http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bulletin of the Iranian Mathematical Society Springer Journals

Nonlinear Generalized Lie Triple Higher Derivation on Triangular Algebras

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Publisher
Springer Journals
Copyright
Copyright © 2018 by Iranian Mathematical Society
Subject
Mathematics; Mathematics, general
ISSN
1017-060X
eISSN
1735-8515
D.O.I.
10.1007/s41980-018-0035-8
Publisher site
See Article on Publisher Site

Abstract

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 .

Journal

Bulletin of the Iranian Mathematical SocietySpringer Journals

Published: Jun 4, 2018

References

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