Quotients and Inverse Limits of Spaces of Orderings

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. N...

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Bibliographic Details
Published in:Canadian journal of mathematics 1979-06, Vol.31 (3), p.604-616
Main Author: Marshall, Murray A.
Format: Article
Language:English
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Summary: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 ).
ISSN:0008-414X
1496-4279
DOI:10.4153/CJM-1979-061-4