Publikation: Some remarks on orderings under finite field extensions
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1992
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Pacific Journal of Mathematics. 1992, 152(1), pp. 175-185. ISSN 0030-8730. eISSN 1945-5844. Available under: doi: 10.2140/pjm.1992.152.175
Zusammenfassung
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.
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510 Mathematik
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SCHEIDERER, Claus, 1992. Some remarks on orderings under finite field extensions. In: Pacific Journal of Mathematics. 1992, 152(1), pp. 175-185. ISSN 0030-8730. eISSN 1945-5844. Available under: doi: 10.2140/pjm.1992.152.175BibTex
@article{Scheiderer1992remar-23330,
year={1992},
doi={10.2140/pjm.1992.152.175},
title={Some remarks on orderings under finite field extensions},
number={1},
volume={152},
issn={0030-8730},
journal={Pacific Journal of Mathematics},
pages={175--185},
author={Scheiderer, Claus}
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<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>
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