2015
DOI: 10.4064/fm229-3-3
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Quotients of index two and general quotients in a space of orderings

Abstract: In our work we investigate quotient structures and quotient spaces of a space of orderings arising from subgroups of index two. We provide necessary and sufficient conditions for a quotient structure to be a quotient space that, among other things, depend on the stability index of the given space. The case of the space of orderings of the field Q(x) is particularly interesting, since then the theory developed simplifies significantly. A part of the theory firstly developed for quotients of index 2 generalizes … Show more

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Cited by 1 publication
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“…Finally, if (X, G) is a space of orderings, by a fan in (X, G) we understand a subspace V such that the space (V, G| V ) is a fan. Sheaves of spaces of orderings had been defined in [4,Chapter 8], where the original results are phrased in terms of reduced Witt rings, and recently studied in [1] and [3]. The definition of the sheaf that we use here is exactly the one taken from [3].…”
mentioning
confidence: 99%
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“…Finally, if (X, G) is a space of orderings, by a fan in (X, G) we understand a subspace V such that the space (V, G| V ) is a fan. Sheaves of spaces of orderings had been defined in [4,Chapter 8], where the original results are phrased in terms of reduced Witt rings, and recently studied in [1] and [3]. The definition of the sheaf that we use here is exactly the one taken from [3].…”
mentioning
confidence: 99%
“…Sheaves of spaces of orderings had been defined in [4,Chapter 8], where the original results are phrased in terms of reduced Witt rings, and recently studied in [1] and [3]. The definition of the sheaf that we use here is exactly the one taken from [3]. Assume (X i , G i ) is a space of orderings for each i ∈ I, where I is a Boolean space.…”
mentioning
confidence: 99%