Some remarks on orderings under finite field extensions

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SCHEIDERER, Claus, 1992. Some remarks on orderings under finite field extensions. In: Pacific Journal of Mathematics. 152(1), pp. 175-185. ISSN 0030-8730. eISSN 1945-5844

@article{Scheiderer1992remar-23330, title={Some remarks on orderings under finite field extensions}, year={1992}, doi={10.2140/pjm.1992.152.175}, number={1}, volume={152}, issn={0030-8730}, journal={Pacific Journal of Mathematics}, pages={175--185}, author={Scheiderer, Claus} }

<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bibo="http://purl.org/ontology/bibo/" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:xsd="http://www.w3.org/2001/XMLSchema#" > <rdf:Description rdf:about="https://kops.uni-konstanz.de/rdf/resource/123456789/23330"> <dc:rights>deposit-license</dc:rights> <dc:language>eng</dc:language> <dcterms:bibliographicCitation>Pacific Journal of Mathemathics ; 152 (1992), 1. - S. 175-185</dcterms:bibliographicCitation> <dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2013-05-17T09:09:29Z</dcterms:available> <dc:creator>Scheiderer, Claus</dc:creator> <dcterms:title>Some remarks on orderings under finite field extensions</dcterms:title> <bibo:uri rdf:resource="http://kops.uni-konstanz.de/handle/123456789/23330"/> <dcterms:issued>1992</dcterms:issued> <dc:contributor>Scheiderer, Claus</dc:contributor> <dcterms:rights rdf:resource="http://nbn-resolving.org/urn:nbn:de:bsz:352-20140905103605204-4002607-1"/> <dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2013-05-17T09:09:29Z</dc:date> <dcterms:abstract xml:lang="eng">Let XK denote the space of orderings of a field K, and rL∕K : XL → XK the restriction mapping, when L∕K is a field extension. Fixing K, the image sets rL∕K(XL) for finite extensions L∕K are investigated. If K is hilbertian, any clopen subset U ⊂ XK has the form U = rL∕K(XL) for some finite L∕K, and [L : K] can be bounded in terms of U. This bound is even sharp in some cases, but not always. A second construction gives the same qualitative result for a much larger class of fields. It is based on iterated quadratic extensions. The bounds on [L : K] obtained here are weaker than in the hilbertian case.</dcterms:abstract> </rdf:Description> </rdf:RDF>

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