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