Nonlinear Lie Triple Higher Derivations on Triangular Algebras by Local Actions: A New Perspective

Let R be a commutative ring with unity and T be a triangular algebra over R. Let a sequence Δ={δn}n∈N of nonlinear mappings δn:T→T is a Lie triple higher derivation by local actions satisfying the equation. Under some mild conditions on T, we prove in this paper that every Lie triple higher derivati...

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Bibliographic Details
Published inAxioms Vol. 11; no. 7; p. 328
Main Authors Liang, Xinfeng, Ren, Dandan, Li, Qingliu
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.07.2022
Subjects
Algebra
Commutativity
Derivation
faithful bimodule
higher derivation
Lie triple higher derivation
local action
Rings (mathematics)
triangular algebras
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Summary:Let R be a commutative ring with unity and T be a triangular algebra over R. Let a sequence Δ={δn}n∈N of nonlinear mappings δn:T→T is a Lie triple higher derivation by local actions satisfying the equation. Under some mild conditions on T, we prove in this paper that every Lie triple higher derivation by local actions on the triangular algebras is proper. As an application, we shall give a characterization of Lie triple higher derivations by local actions on upper triangular matrix algebras and nest algebras, respectively.
ISSN:2075-1680
2075-1680
DOI:10.3390/axioms11070328