Böcker av Lindsay N. Childs

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.

This book is an informal and readable introduction to higher algebra at the post-calculus level. The new examples and theory are built in a well-motivated fashion and made relevant by many applications - to cryptography, coding, integration, history of mathematics, and especially to elementary and computational number theory.

Studies Hopf algebras over valuation rings of local fields and their application to the theory of wildly ramified extensions of local fields. This book shows that Hopf algebras play a natural role in local Galois module theory.