In mathematics, a linked field is a field for which the quadratic forms attached to quaternion algebras have a common property.
[1]: 69 The Albert form for A, B is It can be regarded as the difference in the Witt ring of the ternary forms attached to the imaginary subspaces of A and B.
[2] The quaternion algebras are linked if and only if the Albert form is isotropic.
[1]: 370 Every global and local field is linked since all quadratic forms of degree 6 over such fields are isotropic.
The following properties of F are equivalent:[1]: 342 A nonreal linked field has u-invariant equal to 1,2,4 or 8.