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Finite Spaces of Signatures

Published online by Cambridge University Press:  20 November 2018

Victoria Powers
Victoria Powers*
Affiliation:
Emory University, Atlanta, Georgia
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Marshall's Spaces of Orderings are an abstract setting for the reduced theory of quadratic forms and Witt rings. A Space of Orderings consists of an abelian group of exponent 2 and a subset of the character group which satisfies certain axioms. The axioms are modeled on the case where the group is an ordered field modulo the sums of squares of the field and the subset of the character group is the set of orders on the field. There are other examples, arising from ordered semi-local rings [4, p. 321], ordered skew fields [2, p. 92], and planar ternary rings [3]. In [4], Marshall showed that a Space of Orderings in which the group is finite arises from an ordered field. In further papers Marshall used these abstract techniques to provide new, more elegant proofs of results known for ordered fields, and to prove theorems previously unknown in the field setting.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 41 , Issue 5 , 01 October 1989 , pp. 808 - 829
Copyright
Copyright © Canadian Mathematical Society 1989

References

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