Description

Book Synopsis
Hopf algebras have been shown to play a natural role in studying questions of integral module structure in extensions of local or global fields. This book surveys the state of the art in Hopf-Galois theory and Hopf-Galois module theory.

Table of Contents
  • Introduction: What is this book about?
  • Hopf-Galois extensions: Hopf-Galois structures on Galois extensions of fields, regular subgroups, and skew braces
  • (Non)-existence results on Hopf-Galois structures
  • Hopf-Galois structures arising from fixed point free pairs of homomorphisms
  • Quantitative results
  • Enumeration of Hopf-Galois structures on Galois extenion of degree $mp$
  • On the Galois correspondence for Hopf-Galois structures
  • Normality in Hopf-Galois extensions
  • Descent theory, and the structure of Hopf algebras acting on separable field extensions
  • Hopf-Galois actions on purely inseparable extensions
  • Hopf-Galois module theory: Hopf-Galois module theory
  • Hopf orders in group rings
  • Ramification theory for separable extensions of local fields
  • Stable and semistable Hopf-Galois extensions
  • Hopf-Galois scaffolds
  • Bibliography
  • Index

Hopf Algebras and Galois Module Theory

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    RRP £109.00 – you save £10.90 (10%)

    Order before 4pm today for delivery by Thu 25 Jun 2026.

    A Paperback by Lindsay N. Childs, Cornelius Greither, Kevin P. Keating

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      Publisher: MP-AMM American Mathematical
      Publication Date: 1/30/2022 12:00:00 AM
      ISBN13: 9781470465162, 978-1470465162
      ISBN10: 1470465167

      Description

      Book Synopsis
      Hopf algebras have been shown to play a natural role in studying questions of integral module structure in extensions of local or global fields. This book surveys the state of the art in Hopf-Galois theory and Hopf-Galois module theory.

      Table of Contents
      • Introduction: What is this book about?
      • Hopf-Galois extensions: Hopf-Galois structures on Galois extensions of fields, regular subgroups, and skew braces
      • (Non)-existence results on Hopf-Galois structures
      • Hopf-Galois structures arising from fixed point free pairs of homomorphisms
      • Quantitative results
      • Enumeration of Hopf-Galois structures on Galois extenion of degree $mp$
      • On the Galois correspondence for Hopf-Galois structures
      • Normality in Hopf-Galois extensions
      • Descent theory, and the structure of Hopf algebras acting on separable field extensions
      • Hopf-Galois actions on purely inseparable extensions
      • Hopf-Galois module theory: Hopf-Galois module theory
      • Hopf orders in group rings
      • Ramification theory for separable extensions of local fields
      • Stable and semistable Hopf-Galois extensions
      • Hopf-Galois scaffolds
      • Bibliography
      • Index

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