Quaternion Orders
Date Issued
2005
Date
2005
Author(s)
Sun, Chia-Liang
DOI
en-US
Abstract
The goal of this paper is to introduce the quaternion orders. In Section
ef{basic}, I give a brief introduction to quaternion algebra. Definitions and basic results necessary for the remaining sections are established in a very elementary way. Anyone who has learned one-year undergraduate algebra and knows the definition of tensor product should be able to read it without difficulties. In Section
ef{general}, general properties about the quaternion orders are proven and the Eichler orders are introduced. In Section
ef{rational}, special properties of the quaternion orders over the field of rational numbers are given. Section
ef{local} and
ef{global} are aimed to describe all the Eichler orders over number fields. In Section
ef{local}, we give explicit formulations for the Eichler orders over the local field which is the completion of a number field with respect to one of its metric. In Section
ef{global}, information about the local Eichler orders are collected to get an understanding about the Eichler orders over global fields. Some Eichler orders over the field of rational numbers are given explicitly.
Subjects
四元素代數
秩序
艾克秩序
quaternion algebras
orders
Eichler orders
Type
thesis