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Quotients and Inverse Limits of Spaces of Orderings

Published online by Cambridge University Press:  20 November 2018

Murray A. Marshall
Murray A. Marshall*
Affiliation:
University of Saskatchewan, Saskatoon, Saskatchewan
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A connection between the theory of quadratic forms defined over a given field F, and the space XF of all orderings of F is developed by A. Pfister in [12]. XF can be viewed as a set of characters acting on the group F×/ΣF×2, where ΣF×2 denotes the subgroup of F× consisting of sums of squares. Namely, each ordering P ∈ XF can be identified with the character

defined by

It follows from Pfister's result that the Witt ring of F modulo its radical is completely determined by the pair (XF, F×/ΣF×2).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 31 , Issue 3 , 01 June 1979 , pp. 604 - 616
Copyright
Copyright © Canadian Mathematical Society 1979

References

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