Titlebook: Quaternion Algebras; John Voight Textbook‘‘‘‘‘‘‘‘ 2021 The Editor(s) (if applicable) and The Author(s) 2021 Open Access.Quaternions.Quater

faddish

Colonoscopy

The Hurwitz orderelds and the arithmetic of their orders. Before we do so, for motivation and pure enjoyment, in this chapter we consider the special case of the Hurwitz order. Not only is this appropriate in a historical spirit, it is also instructive for what follows; moreover, the Hurwitz order has certain except

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Quaternion ideals and invertibilityand modules over . (in other words, to pursue “l(fā)inear algebra” over .). The ideals of a ring that are easiest to work with are the principal ideals—but not all ideals are principal, and various algebraic structures are built to understand the difference between these two. In this chapter, we conside

Autobiography

978-3-030-57467-3The Editor(s) (if applicable) and The Author(s) 2021

accessory

BINGE

聯(lián)想記憶

ALE

Simple algebrasns in Chapter .; in the chapters that followed, we showed that quaternion algebras are equivalently noncommutative algebras with a nondegenerate standard involution. Here, we pursue another approach, and we characterize quaternion algebras in a different way, as central simple algebras of dimension 4.

Insufficient

laceration