Splittable Jordan homomorphisms and commutator ideals
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866914968522194944 |
|---|---|
| author | Brešar, Matej |
| author_facet | Brešar, Matej |
| contents | We define a Jordan homomorphism $φ$ from a ring $R$ to a ring $R'$ to be splittable if the ideal (of the subring generated by the image of $φ$) generated by all $φ(xy)-φ(x)φ(y)$, $x,y\in R$, has trivial intersection with the ideal generated by all $φ(xy)-φ(y)φ(x)$, $x,y\in R$. Our main result states that a splittable Jordan homomorphism is the sum of a homomorphism and an antihomomorphism on the commutator ideal. As applications, we obtain results that give new insight into the question of the structure of Jordan homomorphisms on some classes of rings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_07052 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Splittable Jordan homomorphisms and commutator ideals Brešar, Matej Rings and Algebras We define a Jordan homomorphism $φ$ from a ring $R$ to a ring $R'$ to be splittable if the ideal (of the subring generated by the image of $φ$) generated by all $φ(xy)-φ(x)φ(y)$, $x,y\in R$, has trivial intersection with the ideal generated by all $φ(xy)-φ(y)φ(x)$, $x,y\in R$. Our main result states that a splittable Jordan homomorphism is the sum of a homomorphism and an antihomomorphism on the commutator ideal. As applications, we obtain results that give new insight into the question of the structure of Jordan homomorphisms on some classes of rings. |
| title | Splittable Jordan homomorphisms and commutator ideals |
| topic | Rings and Algebras |
| url | https://arxiv.org/abs/2410.07052 |