Advertisement

Epilogue

  • Joseph Rotman
Part of the Universitext book series (UTX)

Abstract

You have seen an introduction to Galois theory; of course, there is more. A deeper study of abelian fields, that is, fields having (possibly infinite) abelian Galois groups, begins with Kummer theory and continues on to class field theory. Infinite Galois groups are topologized, and there is a bijection between intermediate fields and closed subgroups. The theorems are of basic importance in algebraic number theory. There is also a Galois theory classifying division algebras (see [Jacobson (1956)] and a Galois theory classifying commutative rings (see [Chase, Harrison, Rosenberg]).

Keywords

Fundamental Group Commutative Ring Galois Group Closed Subgroup Galois Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Copyright information

© Springer-Verlag New York Inc. 1990

Authors and Affiliations

  • Joseph Rotman
    • 1
  1. 1.Department of MathematicsUniversity of Illinois at Urbana-ChampaignUrbanaUSA

Personalised recommendations