Forms and Baer ordered *-fields

It is well known that for a quaternion algegra, the anisotropy of its norm form determines if the quaternion algebra is a division algebra. In case of biquaternio algebra, the anisotropy of the associated Albert form (as defined in LLT]) determines if the biquaternion algebra is a division ring. In these situations, the norm forms and the Albert forms are quadratic forms over the center of the quaternion algebras; and they are strongly related to the algebraic structure of the algebras. As it turns out, there is a natural way to associate a tensor product of quaternion algebras with a form such that when the involution is orthogonal, the algebra is a Baer ordered *-field iff the associated form is anisotropic.