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.
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