Solvability of commutative power-associative nilalgebras of nilindex 4 and dimension

Author
Elgueta, Luisa

Suazo Delgado, Avelino

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https://www.revistaproyecciones.cl/article/view/1564
10.4067/S0716-09172004000200005
Abstract
Let A be a commutative power-associative nilalgebra. In this paper we prove that when A (of characteristic ≠2) is of dimension ≤ 8 and x⁴ = 0 for all x ∈ A, then ((A²)²)² = 0. That is, A is solvable. We conclude that if A is of dimension ≤ 7 over a field of characteristic ≠2, 3 and 5, then A is solvable.
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