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Hopf Orders and Galois Module Theory

In: An Introduction to Hopf Algebras

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  • Robert G. Underwood

    (Auburn University, Department of Mathematics)

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.

Suggested Citation

  • Robert G. Underwood, 2011. "Hopf Orders and Galois Module Theory," Springer Books, in: An Introduction to Hopf Algebras, chapter 0, pages 195-231, Springer.
    • Handle: RePEc:spr:sprchp:978-0-387-72766-0_10
    DOI: 10.1007/978-0-387-72766-0_10
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