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Thursday 11 Jul 2019Hopf-Galois module structure of a class of tame quaternion fields

Paul Truman - Keele University

Amory C417 15:15-16:15

We call a Galois extension of the rational numbers with Galois group isomorphic to the quaternion group of order 8 a quaternion field. Certain tamely ramified quaternion fields provided the first examples of tame Galois extensions of the rational numbers with no normal integral basis; loosely, the algebraic integers in these examples are described poorly by classical Galois theory. In this talk we use Hopf-Galois theory to study some of these examples, and investigate whether this approach results in a more satisfactory description of the algebraic integers.

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