Search results for "tag:"Author Kevin Childs""

Book SynopsisHopf 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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