Abstract

ELGUETA, LUISA  and  SUAZO, AVELINO. On the Solvability of Commutative Power-Associative Nilalgebras of Nilindex 4. Rev.colomb.mat. [online]. 2010, vol.44, n.2, pp.119-128. ISSN 0034-7426.

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.

Keywords : Commutative; Power-associative; Nilalgebra; Solvable; Nilpotent.

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