Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-26T04:44:36.043Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

1. Baeza, R. and Knebusch, M., Annullatoren von Pfisterformen ilber semilokalen ringen, Math. Zeit. 140 (1974), 41–62.Google Scholar
2. Becker, E. and Brocker, L., On the description of the reduced Witt rings, J. Alg. 52. 2 (1978), 328–346.Google Scholar
3. Brôcker, L., Zur théorie der quadratischen formen iiber formal reelen korpern, Math. Ann. 210 (1974), 233–256.Google Scholar
4. Brôcker, L., Characterization of fans and hereditarily Pythagorian fields, Math. Zeit. 152 (1976), 149–163.Google Scholar
5. Brôcker, L., Uber die anzahl der anordnungen eines kommutativen korpers, Archiv der Math. 29 (1977), 458–464.Google Scholar
6. Craven, T., The Boolean space of orderings of a field, Trans. Amer. Math. Soc. 209 (1975), 225–235.Google Scholar
7. Craven, T., Characterizing reduced Witt rings of fields, J. of Alg. 53 (1978), 68–77.Google Scholar
8. Knebusch, M., Rosenberg, A. and Ware, R., Signatures on semilocal rings, Bull, of Amer. Math. Soc. 78. 1 (1972), 62–64.Google Scholar
9. Marshall, M., A reduced theory of quadratic forms, Conference on Quadratic Forms, Queen's Papers in pure and applied mathematics, 46 (1977), 569–579, Queens’ University.Google Scholar
10. Marshall, M., Some local-global principles for formally real fields, Can. J. Math. 29, No. 3 (1977), 606–614.Google Scholar
11. Marshall, M., Classification of finite spaces of orderings, to appear.Google Scholar
12. Pfister, A., Quadratische formen in beliebigen kôrpern, Invent. Math. 1 (1966), 116–132.Google Scholar
13. Prestel, A., Lectures on formally real fields, lecture notes, IM PA.Google Scholar