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arXiv · 2501.19078

Generalized Jordan derivations of unital algebras

Dominik Benkovič·Mateja Grašič
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Abstract

Let $A$ be a unital algebra over a field $F$ with $\operatorname*{char} (F)\neq2$. In this paper we introduce a new concept of a generalized Jordan derivation, covering Jordan centralizers and Jordan derivations, as follows: a linear map $f:A\rightarrow A$ is a generalized Jordan derivation if there exist linear maps $g;h:A\rightarrow A$ such that $f\left( x\right) \circ y+x\circ g\left( y\right) =h\left( x\circ y\right) $ for all $x,y\in A$ (here $x\circ y=xy+yx$). Our aim is to give the form of map $f$ in terms of the so called quasi Jordan centralizers and quasi Jordan derivations. In addition, a characterization of such maps is presented.

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Dominik Benkovič, Mateja Grašič. 2025-01-31. Generalized Jordan derivations of unital algebras. https://arxiv.org/abs/2501.19078

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