The goal of this paper is to
explore the connection between three properties of a field F of characteristic not 2.
Roughly speaking, these are:
the Witt ring W(F) is a group ring R[G] with G an Abelian group of
exponent 2.
the Witt ring W(F) is isomorphic to W(K) where K is a power series
field (i.e., F is equivalent to K with respect to quadratic forms).
there are “enough” rigid elements in F.
Our purpose is to show that the connection is in some sense “quantitative”, by
showing that (a) and (b) can be “measured” by the index of a certain subgroup A(F)
in Ḟ.
