Jordan higher derivations on some matrix algebras

Document Type : Original Article

Author

School of Mathematics and Computer Science, Damghan University, Damghan, Iran

Abstract

In this article, we study Jordan higher derivations on unital algebras with non-trivial idempotent. We extend some previous results on Jordan derivations of such algebras to Jordan higher derivations and show that, under mild conditions, every Jordan higher derivation on a unital algebra with a non-trivial idempotent is a higher derivation. We apply this result to  several classes of matrix algebras, including the triangular algebra $\mathrm{Tri}(A, X, B)$, the algebra of upper triangular matrices $T_n(\cR)$, and the nest algebra $T(\cN)$. This allows us to extend previous results on Jordan derivations to Jordan higher derivations for these algebras.

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References

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Measure Algebras and Applications
Volume 2, Issue 2 - Serial Number 3
December 2024
Pages 94-105

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History

  • Receive Date: 12 August 2024
  • Revise Date: 09 November 2024
  • Accept Date: 18 November 2024

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