Vol. 89, No. 2, 1980

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Quadratic forms and power series fields

Lawrence Victor Berman

Vol. 89 (1980), No. 2, 257–267

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:

  1. the Witt ring W(F) is a group ring R[G] with G an Abelian group of exponent 2.
  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).
  3. 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 .

Mathematical Subject Classification
Primary: 10C05, 10C05
Received: 11 June 1979
Published: 1 August 1980
Lawrence Victor Berman