Solvability of a Commutative Algebra which Satisfies (x 2)2 = 0

Abstract

We studied the solvability of the algebra which satisfies the polynomial identity (x 2)2 = 0. We believe that, if A is a finite dimensional commutative algebra over a field F of characteristic not 2 which satisfies (x 2)2 = 0 for all x ∈ A, then A is solvable. In this article we proved this when dim  F A ≤ 7.