Hopf Orders and Galois Module Theory

Abstract

For this chapter, we return to the global situation where K is a finite extension of $\mathcal{Q}$, R is the integral closure of $\mathcal{Z}$ in K, and L is a Galois extension of K with group G and ring of integers S. In this chapter, we study applications of Hopf orders to Galois module theory. Galois module theory is the branch of number theory that seeks to describe S as a module over the group ring RG. We begin with a review of some Galois theory.