On linear dependence of roots
On nilpotent Galois groups and the scope of the norm limitation theorem in one-dimensional abstract local class field theory.
On normal binomials
On p-groups as Galois groups.
On places of algebraic function fields.
On prosolvable subgroups of profinite free products and some applications.
On rank of extensions of valuations
On realizability of p-groups as Galois groups
2000 Mathematics Subject Classification: 12F12, 15A66.In this article we survey and examine the realizability of p-groups as Galois groups over arbitrary fields. In particular we consider various cohomological criteria that lead to necessary and sufficient conditions for the realizability of such a group as a Galois group, the embedding problem (i.e., realizability over a given subextension), descriptions of such extensions, automatic realizations among p-groups, and related topics.
On Relations Between Zeros of Galois Polynomials.
On relative integral bases for unramified extensions
0. Introduction. Since ℤ is a principal ideal domain, every finitely generated torsion-free ℤ-module has a finite ℤ-basis; in particular, any fractional ideal in a number field has an "integral basis". However, if K is an arbitrary number field the ring of integers, A, of K is a Dedekind domain but not necessarily a principal ideal domain. If L/K is a finite extension of number fields, then the fractional ideals of L are finitely generated and torsion-free (or, equivalently, finitely generated and...
On ruled fields
Some results and problems that arise in connection with the foundations of the theory of ruled and rational field extensions are discussed.
On Sign Determinations in Real Algebraic Number Fields.
On Solvability by Radicals of Field Extensions.
On Solvability by Radicals of Finite Fields.
On some characterizations of the complex number field
On subfields of
On the Beckmann-Black problem
On the class numbers of certain Hilbert class fields.
On the compositum of all degree extensions of a number field
We study the compositum of all degree extensions of a number field in a fixed algebraic closure. We show contains all subextensions of degree less than if and only if . We prove that for there is no bound on the degree of elements required to generate finite subextensions of . Restricting to Galois subextensions, we prove such a bound does not exist under certain conditions on divisors of , but that one can take when is prime. This question was inspired by work of Bombieri and...
On the computation of resolvents and Galois groups.