On the Solvability of Commutative Power-Associative Nilalgebras of Nilindex 4

Publicado

2010-07-01

On the Solvability of Commutative Power-Associative Nilalgebras of Nilindex 4

Palabras clave:

Commutative, Power-associative, Nilalgebra, Solvable, Nilpotent (es)

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Autores/as

Luisa Elgueta Universidad de La Serena
Avelino Suazo Universidad de La Serena

Resumen (en)

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.