Fields: Algebraically closed and others.
Fields containing values of algebraic functions
Fields containing values of algebraic functions II (On a conjecture of Schinzel)
Frattini Covers and Projective Groups Without the Extension Property.
Galois theory for general extension fields.
Halbordnungen und maximale Teilkörper in gelochten algebraisch-abgeschlossenen Körpern.
Heckesche Systeme idealer Zahlen und Knesersche Körpererweiterungen
Einleitung. Eine klassische Konstruktion aus der algebraischen Zahlentheorie ist folgende: Zu jedem algebraischen Zahlkörper K kann man ein sogenanntes System idealer Zahlen S zuordnen, welches eine Untergruppe der multiplikativen Gruppe ℂ* der komplexen Zahlen ist derart, daß die Faktorgruppe S/K* in kanonischer Weise isomorph zu der Klassengruppe von K ist. Diese Konstruktion geht auf Hecke [5] zurück und hat folgende wichtige Eigenschaft, die auch bei dem Hilbertschen Klassenkörper zu K vorkommt:...
Higher degree Harrison equivalence and Milnor -functor
How Many Algebraic (Finite) Extensions Over The Rationals
How many algebraic (finite) extensions over the rationals.
Invariante Zwischenkörper endlicher Körpererweiterungen.
Irreducible polynomials over finite fields with linearly independent roots
Lagrange Resolvents.
L’azione del gruppo simplettico associata ad un’estensione quadratica di campi
Neuer Beweis des Vorhandenseins complexer Wurzeln in einer algebraischen Gleichung. Von Hermann Kinkelin in Basel
Noncyclic Division Algebras.
Norms in Quadratic Fields and Their Relations to Non Commuting 2x2 Matrices I.
Note on a variation of the Schröder-Bernstein problem for fields
In this note we study fields with the property that the simple transcendental extension of is isomorphic to some subfield of but not isomorphic to . Such a field provides one type of solution of the Schröder-Bernstein problem for fields.
On algebraic closures.
This is a description of some different approaches which have been taken to the problem of generalizing the algebraic closure of a field. Work surveyed is by Enoch and Hochster (commutative algebra), Raphael (categories and rings of quotients), Borho (the polynomial approach), and Carson (logic).Later work and applications are given.
On degrees of three algebraic numbers with zero sum or unit product
Let α, β and γ be algebraic numbers of respective degrees a, b and c over ℚ such that α + β + γ = 0. We prove that there exist algebraic numbers α₁, β₁ and γ₁ of the same respective degrees a, b and c over ℚ such that α₁ β₁ γ₁ = 1. This proves a previously formulated conjecture. We also investigate the problem of describing the set of triplets (a,b,c) ∈ ℕ³ for which there exist finite field extensions K/k and L/k (of a fixed field k) of degrees a and b, respectively, such that the degree of the...