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


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]).


Fundamental Group Commutative Ring Galois Group Closed Subgroup Galois Theory 
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Copyright information

© Springer-Verlag New York Inc. 1990

Authors and Affiliations

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

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