A Frattini theory for evolution algebras
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866909673439887360 |
|---|---|
| author | Ladra, Manuel Pérez-Rodríguez, Andrés |
| author_facet | Ladra, Manuel Pérez-Rodríguez, Andrés |
| contents | This paper develops a Frattini theory for evolution algebras defining the Frattini subalgebra as the intersection of all maximal subalgebras, and the Frattini ideal as the largest ideal contained in it. To this end, we revisit the notion of nilradical, whose classical definition is not directly applicable in this setting, and propose the supersolvable nilradical as a suitable alternative. This leads to necessary and sufficient conditions for the triviality of the Frattini subalgebra and ideal. Finally, we also briefly examine the relevance of the Frattini ideal in the study of dually atomistic evolution algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_01935 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Frattini theory for evolution algebras Ladra, Manuel Pérez-Rodríguez, Andrés Rings and Algebras 17D92, 17A60, 17B30, 06B05 This paper develops a Frattini theory for evolution algebras defining the Frattini subalgebra as the intersection of all maximal subalgebras, and the Frattini ideal as the largest ideal contained in it. To this end, we revisit the notion of nilradical, whose classical definition is not directly applicable in this setting, and propose the supersolvable nilradical as a suitable alternative. This leads to necessary and sufficient conditions for the triviality of the Frattini subalgebra and ideal. Finally, we also briefly examine the relevance of the Frattini ideal in the study of dually atomistic evolution algebras. |
| title | A Frattini theory for evolution algebras |
| topic | Rings and Algebras 17D92, 17A60, 17B30, 06B05 |
| url | https://arxiv.org/abs/2507.01935 |