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Generalized Higher Derivations on Lie Ideals of Triangular Algebras

Mohammad Ashraf; Nazia Parveen; Bilal Ahmad Wani — 2017

Communications in Mathematics

Let $𝔄 = (\begin{matrix} 𝒜 & ℳ \\ ℬ \end{matrix})$ be the triangular algebra consisting of unital algebras $𝒜$ and $ℬ$ over a commutative ring $R$ with identity $1$ and $ℳ$ be a unital $(𝒜, ℬ)$ -bimodule. An additive subgroup $𝔏$ of $𝔄$ is said to be a Lie ideal of $𝔄$ if $[𝔏, 𝔄] \subseteq 𝔏$ . A non-central square closed Lie ideal $𝔏$ of $𝔄$ is known as an admissible Lie ideal. The main result of the present paper states that under certain restrictions on $𝔄$ , every generalized Jordan triple higher derivation of $𝔏$ into $𝔄$ is a generalized higher derivation of $𝔏$ into $𝔄$ .

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