On the structure of Pythagorean fields
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TL;DR: In this article, the relationship between fans and valuations was studied in detail, where the authors constructed the valuations by "brute force" from the properties of the fields involved, which can be directly related to the structure theory for spaces of orderings developed by Murray Marshall.
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About: This article is published in Journal of Algebra. The article was published on 01 Feb 1981. and is currently open access. The article focuses on the topics: Pythagorean theorem & Structure (category theory).
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Citations
Powers of totally positive subgroups of fields
TL;DR: For a real field F, a totally positive co-torsion subgroup S of F × and m ⩾ 1, it was shown in this article that ( ∑ S ) m ⊆ ∑ s m.
References
Cohomology of group extensions
G. Hochschild,Jean-Pierre Serre +1 more
TL;DR: In this article, the Cartan-Leray spectral sequence is generalized to other algebraic situations, as will be shown in a forthcoming paper of Cartan Eilenberg [2].
Classification of Finite Spaces of Orderings
TL;DR: In this article, a set of quasi-orderings is defined as a pair (X, G) where G is an elementary 2-group with a distinguished element, and X is a subset of the character group x(G) = Horn (G, {1, 1, 1}.
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