On Algebras Satisfying the Identity $(yx)x + x(xy) = 2(xy)x

Simple, strictly power-associative algebras satisfying the identity $(yx)x + x(xy) = 2(xy)x$ 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.