The universal invariant u(F) of a field F is the largest dimension of an anisotropic quadratic space over F, or ∞ if this does not exist.
In the case of quadratic extensions, the u-invariant is bounded by and all values in this range are achieved.
[11] Since the u-invariant is of little interest in the case of formally real fields, we define a general u-invariant to be the maximum dimension of an anisotropic form in the torsion subgroup of the Witt ring of F, or ∞ if this does not exist.
[12] For non-formally-real fields, the Witt ring is torsion, so this agrees with the previous definition.
[13] For a formally real field, the general u-invariant is either even or ∞.