Abstract
We study third-power associative division algebras A over a field 𝕂 of characteristic different from 2. Those algebras having dimension ≤2 are commutative. When 𝕂 is the field ℝ of real numbers, those algebras having dimension 4 are power-commutative in each of the following two cases:A contains a central element;A satisfies the additional identity (x, x3, x) = 0.
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