A note on generalized Jordan n-derivations of unital rings

Let R be a unital ring. We show that under suitable assumptions every generalized Jordan n -derivation f : R → R is of the form f ( x ) = λ x + d ( x ) , where λ ∈ Z ( R ) and d : R → R is a Jordan derivation. As an application, we give a description of generalized Jordan n -derivations on semiprime...

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Bibliographic Details
Published in:Indian journal of pure and applied mathematics 2024-06, Vol.55 (2), p.623-627
Main Author: Benkovič, Dominik
Format: Article
Language:English
Subjects:
Applications of Mathematics
Derivation
Mathematics
Mathematics and Statistics
Numerical Analysis
Original Research
Rings (mathematics)
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Summary:Let R be a unital ring. We show that under suitable assumptions every generalized Jordan n -derivation f : R → R is of the form f ( x ) = λ x + d ( x ) , where λ ∈ Z ( R ) and 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.
ISSN:0019-5588
0975-7465
DOI:10.1007/s13226-023-00394-2