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Journal of Pure and Applied Algebra 189 (2004) 15 www.elsevier.com/locate/jpaa

Summary: Journal of Pure and Applied Algebra 189 (2004) 1­5
P˙ster's subform theorem for reduced
special groups
Vincent Astier
NWF I - Mathematik, Universitat Regensburg, Regensburg 93040, Germany
Received 22 November 2001; received in revised form 17 September 2003
Communicated by M.-F. Roy
P˙ster's subform theorem is an essential result in the theory of quadratic forms, but its proof uses
transcendental ˙eld extensions which have no equivalent in the axiomatic theory. We present here
a proof of this result for reduced special groups/spaces of orderings which avoids this di culty.
c 2003 Elsevier B.V. All rights reserved.
MSC: 11E81; 03C65
1. Introduction
The algebraic theory of quadratic forms admits several axiomatizations, for exam-
ple abstract Witt rings, special groups, or, for the reduced theory, abstract spaces of
orderings (these axiomatizations are essentially equivalent).
They provide the usual advantages such as uni˙ed proofs, but the question of whether
or not they exactly describe the theory of quadratic forms over ˙elds (i.e. is every


Source: Astier, Vincent - Department of Mathematics, University College Dublin


Collections: Mathematics