Journal or Book Title
Journal of Algebra and Its Applications
We determine the identities of degree ≤ 6 satisfied by the symmetric (Jordan) product a○b = ab + ba and the associator [a,b,c] = (ab)c - a(bc) in every nonassociative algebra. In addition to the commutative identity a○b = b○a we obtain one new identity in degree 4 and another new identity in degree 5. We demonstrate the existence of further new identities in degree 6. These identities define a variety of binary-ternary algebras which generalizes the variety of Jordan algebras in the same way that Akivis algebras generalize Lie algebras.
World Scientific Publishing
Bremner, Murray R. and Hentzel, Irvin R., "Identities relating the Jordan product and the associator in the free nonassociative algebra" (2006). Mathematics Publications. 132.