Generalised quadratic forms and the u-invariant.

The u -invariant of a field is the supremum of the dimensions of anisotropic quadratic forms over the field. We define corresponding u -invariants for hermitian and generalised quadratic forms over a division algebra with involution in characteristic 2 and investigate the relationships between them. We investigate these invariants in particular in the case of a quaternion algebra and further when this quaternion algebra is the unique quaternion division algebra over a field. [ABSTRACT FROM AUTHOR]