Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

A Galois approach to Kaplansky Radical $\times$ Hilbert's Theorem 90

Ronie Peterson Dario

Abstract

This paper aims to prove a version of the Hilbert's Theorem 90 for a field with non-trivial Kaplansky radical and the Galois group of its maximal $2$-extension as a finitely generated elementary type pro-2 group.

A Galois approach to Kaplansky Radical $\times$ Hilbert's Theorem 90

Abstract

This paper aims to prove a version of the Hilbert's Theorem 90 for a field with non-trivial Kaplansky radical and the Galois group of its maximal -extension as a finitely generated elementary type pro-2 group.

Paper Structure

This paper contains 9 sections, 15 theorems, 18 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Basic groups and the Kaplansky radical
  4. The elementary type conjecture for Galois groups
  5. Basic operations and the Kaplansky radical
  6. Free pro-$2$ products
  7. Semi-direct products and valuations
  8. The Kaplansky radical and ETG groups
  9. The Hilbert's Theorem 90

Key Result

Theorem 1

Conjecture claimh90 is true for a field $F$ such that $G_F(2)$ is an ETG group.

Theorems & Definitions (41)

  • Conjecture 1
  • Theorem
  • Definition 1
  • Example 2
  • Example 3
  • Example 4
  • Example 5
  • Example 6
  • Definition 7
  • Example 8
  • ...and 31 more