Chapter One

Basic Definitions

Gal(L/K)¹) or L is quaternion and is its standard involution as defined in 1.9 (in which case K = Z(L)). Suppose that (L, ) is quadratic and let

1Let F = {}. Then F is a subfield of L and L/F is a separable quadratic extension. Since the map from L to F is linear over F and not the 0-map, it is onto. Thus K = F.

2i.e.