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Classification of Finite Spaces of Orderings

Published online by Cambridge University Press:  20 November 2018

Murray Marshall
Murray Marshall*
Affiliation:
University of Saskatchewan, Saskatoon, Saskatchewan
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1. Introduction. A space of orderings will refer to what was called a “set of quasi-orderings” in [5]. That is, a space of orderings is a pair (X, G) where G is an elementary 2-group (i.e. x2 = 1 for all x ∈ G) with a distinguished element – 1 ∈ G, and X is a subset of the character group x(G) = Horn (G, {1, –1};) satisfying the following properties:

01: X is a closed subset of χ(G).

02: σ(−l) = −1 holds for all σ ∊ X.

03: X⊥ = {a ∊ G|χa = 1 for all a ∊ X} = 1.

04: If f and g are forms over G and if x ∊ Df⊗g, then there exist y ∊ Df and z ∊ Dg such that x ∊ D(y, z).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 31 , Issue 2 , 01 April 1979 , pp. 320 - 330
Copyright
Copyright © Canadian Mathematical Society 1979

References

1. Baeza, R. and Knebusch, M., Annullatoren von Pfisterformen iiber semilokalen ringen, Math. Z. 140 (1974), 41–62.Google Scholar
2. Brôcker, L., Uber die anzahl der anordnungen eines kommutativen kôrpens, Archiv der Math.. 29 (1977), 458–464.Google Scholar
3. Craven, T., Characterizing reduced Witt rings 0﹜fields, J. of Alg. 58 (1978), 68–77.Google Scholar
4. Knebusch, M., Rosenberg, A. and Ware, R., Signatures on semilocal rings, Bull, of the Amer. Math. Soc. Vol. 78. 1 (1972), 62–64.Google Scholar
5. Marshall, M., A reduced theory 0﹜ quadratic forms, unpublished notes.Google Scholar
6. Pfister, A., Quadratische formen in beliebigen korpern, Invent. Math. 1 (1966), 116–132.Google Scholar
7. Witt, E., Théorie der quadratischen formen in beliebigen kôrpern, J. Reine Angew. Math. 176 (1937), 31–44.Google Scholar