On the solvability of commutative power-associative nilalgebras of nilindex 4
Let $A$ be a commutative power-associative nilalgebra. In this paper we prove that when $A$ (of characteristic $\neq 2)$ is of dimension $\leq 10$ and the identity $x^{4}=0$ is valid in $A$, then $((y^{2})x^{2})x^{2}=0$ for all $y$, $x$ in $A$ and $((A^{2})^{2})^{2}=0$. That is, $A$ is solvable.
- Autores:
-
Elgueta, Luisa
Suazo, Avelino
- Tipo de recurso:
- Article of journal
- Fecha de publicación:
- 2010
- Institución:
- Universidad Nacional de Colombia
- Repositorio:
- Universidad Nacional de Colombia
- Idioma:
- spa
- OAI Identifier:
- oai:repositorio.unal.edu.co:unal/39778
- Acceso en línea:
- https://repositorio.unal.edu.co/handle/unal/39778
http://bdigital.unal.edu.co/29875/
- Palabra clave:
- Commutative
Power-associative
Nilalgebra
Solvable
Nilpotent
17A05
17A30
- Rights
- openAccess
- License
- Atribución-NoComercial 4.0 Internacional
| Summary: | Let $A$ be a commutative power-associative nilalgebra. In this paper we prove that when $A$ (of characteristic $\neq 2)$ is of dimension $\leq 10$ and the identity $x^{4}=0$ is valid in $A$, then $((y^{2})x^{2})x^{2}=0$ for all $y$, $x$ in $A$ and $((A^{2})^{2})^{2}=0$. That is, $A$ is solvable. |
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