Thursday 11 Jul 2019: Hopf-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.