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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2501.19078 |
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| _version_ | 1866916592209625088 |
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| author | Benkovič, Dominik Grašič, Mateja |
| author_facet | Benkovič, Dominik Grašič, Mateja |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_19078 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Generalized Jordan derivations of unital algebras Benkovič, Dominik Grašič, Mateja Rings and Algebras 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. |
| title | Generalized Jordan derivations of unital algebras |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2501.19078 |