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Generalized Jordan N-Derivations of Unital Algebras with Idempotents

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  • Xinfeng Liang
  • Ji Gao

Abstract

Let A be a unital algebra with idempotent e over a 2-torsionfree unital commutative ring ℛ and S:A⟶A be an arbitrary generalized Jordan n-derivation associated with a Jordan n-derivation J. We show that, under mild conditions, every generalized Jordan n-derivation S:A⟶A is of the form Sx=λx+Jx in the current work. As an application, we give a description of generalized Jordan derivations for the condition n=2 on classical examples of unital algebras with idempotents: triangular algebras, matrix algebras, nest algebras, and algebras of all bounded linear operators, which generalize some known results.

Suggested Citation

  • Xinfeng Liang & Ji Gao, 2021. "Generalized Jordan N-Derivations of Unital Algebras with Idempotents," Journal of Mathematics, Hindawi, vol. 2021, pages 1-5, June.
    • Handle: RePEc:hin:jjmath:9997646
    DOI: 10.1155/2021/9997646
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    Cited by:

    1. Shakir Ali & Amal S. Alali & Vaishali Varshney, 2024. "Linear Generalized n -Derivations on C ∗ -Algebras," Mathematics, MDPI, vol. 12(10), pages 1-11, May.

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