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