Summary: Generic splitting for special groups
Fachbereich Mathematik und Statistik, D203
Using model-theoretic tools, we present a generalisation of the theory of generic
splitting of quadratic forms to special groups, an axiomatic version of the algebraic
theory of quadratic forms.
Key words: quadratic forms, special groups, generic splitting
1991 MSC: 11E81, 03C65
The algebraic theory of quadratic forms over fields (of characteristic different
from 2) has been introduced by Witt in the 1930's, and has been extensively
studied since. It has also been the object of several axiomatisations, and this
paper concentrates on one of them, the theory of special groups, developed by
Dickmann and Miraglia (see ). This theory is equivalent to the theory of
abstract Witt rings (see ), whose language we will occasionally use, in the
sense that they define isomorphic categories.