¹Universidad de La Serena, La Serena, Chile. Email: lelgueta@userena.cl
²Universidad de La Serena, La Serena, Chile. Email: asuazo@userena.cl

Let A be a commutative power-associative nilalgebra. In this paper we prove that when A (of characteristic ≠ 2) is of dimension ≤ 10 and the identity x⁴=0 is valid in A, then ((y²)x²)x²=0 for all y, x in A and ((A²)²)²=0. That is, A is solvable.

Key words: Commutative, Power-associative, Nilalgebra, Solvable, Nilpotent.

Sea A una nilágebra conmutativa de potencias asociativas. En este trabajo demostramos que cuando A (de característica ≠ 2) es de dimensión ≤ 10 y la identidad x⁴=0 es válida en A, entonces ((y²)x²)x²=0 para todo y, x en A y ((A²)²)²=0. Es decir, A es soluble.

Palabras clave: Conmutativa, potencias asociativas, nilálgebra, soluble, nilpotente.

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References

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