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Simple, strictly power-associative algebras satisfying the identity      ( y x ) x + x ( x y ) = 2 ( x y ) x (yx)x + x(xy) = 2(xy)x       over a field of characteristic not 2 or 3 have been classified by F. Kosier as commutative Jordan, quasi-associative, or of degree less than three. In the present paper those of degree three or greater are shown to be commutative, which eliminates the quasi-associative case mentioned above.

On algebras satisfying the identity (𝑦𝑥)𝑥+𝑥(𝑥𝑦)=2(𝑥𝑦)𝑥