Fully noncentral Lie ideals and invariant additive subgroups in rings
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866929737053503488 |
|---|---|
| author | Gardella, Eusebio Lee, Tsiu-Kwen Thiel, Hannes |
| author_facet | Gardella, Eusebio Lee, Tsiu-Kwen Thiel, Hannes |
| contents | We prove conditions ensuring that a Lie ideal or an invariant additive subgroup in a ring contains all additive commutators. A crucial assumption is that the subgroup is fully noncentral, that is, its image in every quotient is noncentral.
For a unital algebra over a field of characteristic $\neq 2$ where every additive commutator is a sum of square-zero elements, we show that a fully noncentral subspace is a Lie ideal if and only if it is invariant under all inner automorphisms. This applies in particular to zero-product balanced algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_03362 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fully noncentral Lie ideals and invariant additive subgroups in rings Gardella, Eusebio Lee, Tsiu-Kwen Thiel, Hannes Rings and Algebras Operator Algebras Primary 16N60, 16W10. Secondary 16S50, 16W20, 17B60 We prove conditions ensuring that a Lie ideal or an invariant additive subgroup in a ring contains all additive commutators. A crucial assumption is that the subgroup is fully noncentral, that is, its image in every quotient is noncentral. For a unital algebra over a field of characteristic $\neq 2$ where every additive commutator is a sum of square-zero elements, we show that a fully noncentral subspace is a Lie ideal if and only if it is invariant under all inner automorphisms. This applies in particular to zero-product balanced algebras. |
| title | Fully noncentral Lie ideals and invariant additive subgroups in rings |
| topic | Rings and Algebras Operator Algebras Primary 16N60, 16W10. Secondary 16S50, 16W20, 17B60 |
| url | https://arxiv.org/abs/2409.03362 |