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Displaying 81 – 97 of 97

Summen n-ter Potenzen in Körpern.

Eberhard Becker (1979)

Journal für die reine und angewandte Mathematik

Sums of mixed powers in fields and orderings of prescribed level.

Ralph Berr (1992)

Mathematische Zeitschrift

Sur le groupe unitaire relatif à une involution d’un corps algébriquement clos

Bruno Deschamps (2011)

Journal de Théorie des Nombres de Bordeaux

Dans cet article, nous tentons de généraliser à d’autres situations l’isomorphisme de groupes topologiques qui existe entre le groupe $ℝ / ℤ$ et le groupe unitaire $𝕌 = {z \in ℂ / | z | = 1}$ .Nous montrons que cet isomorphisme existe algébriquement en toute généralité : pour tout corps algébriquement clos $C$ et toute involution $c$ de $C$ les groupes $𝕌 (C, c) = {z \in C / z c (z) = 1}$ et $C^{< c >} / ℤ$ sont isomorphes. Nous donnons ensuite un exemple d’involution $c_{0}$ de $ℂ$ qui n’est pas conjuguée, dans le groupe $Aut (ℂ)$ , à la conjugaison complexe et telle que $𝕌 (ℂ, c_{0})$ soit topologiquement isomorphe...

Symmetric and Asymmetric Gaps in Some Fields of Formal Power Series

Galanova, N. (2004)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 03E04, 12J15, 12J25.We consider a construction of fields with symmetric gaps that are not semi-η1. By this construction we give examples of fields with different asymmetric gaps.

The Field of Reals with a Predicate for the Powers of Two.

Lou van den Dries (1986)

Manuscripta mathematica

The Joly–Becker theorem for $*$ –orderings

Igor Klep, Dejan Velušček (2008)

Annales de la faculté des sciences de Toulouse Mathématiques

We prove the $*$ –version of the Joly–Becker theorem: a skew field admits a $*$ –ordering of level $n$ iff it admits a $*$ –ordering of level $n ℓ$ for some (resp. all) odd $ℓ \in ℕ$ . For skew fields with an imaginary unit and fields stronger results are given: a skew field with imaginary unit that admits a $*$ –ordering of higher level also admits a $*$ –ordering of level $1$ . Every field that admits a $*$ –ordering of higher level admits a $*$ –ordering of level $1$ or $2$

The limit behaviour of exponential terms

Bernd Dahn (1984)

Fundamenta Mathematicae

Topology on ordered fields

Yoshio Tanaka (2012)

Commentationes Mathematicae Universitatis Carolinae

An ordered field is a field which has a linear order and the order topology by this order. For a subfield $F$ of an ordered field, we give characterizations for $F$ to be Dedekind-complete or Archimedean in terms of the order topology and the subspace topology on $F$ .