A note on generalized Jordan n-derivations of unital rings

Dominik Benkovič ()
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Dominik Benkovič: University of Maribor

Indian Journal of Pure and Applied Mathematics, 2024, vol. 55, issue 2, 623-627

Abstract: Abstract Let R be a unital ring. We show that under suitable assumptions every generalized Jordan n-derivation $$f:R\rightarrow R$$ f : R → R is of the form $$f(x)=\lambda x+d(x)$$ f ( x ) = λ x + d ( x ) , where $$\lambda \in Z(R)$$ λ ∈ Z ( R ) and $$d:R\rightarrow R$$ d : R → R is a Jordan derivation. As an application, we give a description of generalized Jordan n-derivations on semiprime rings and rings containing nontrivial idempotens, such as triangular rings and matrix rings.

Keywords: Generalized Jordan n-derivation; Jordan derivation; Derivation; Centralizer; Unital ring; 16W25; 16W10 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s13226-023-00394-2

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