Definition:Hurwitz Quaternion

Definition
A Hurwitz quaternion is a quaternion whose components are all either:
 * integers

or:
 * integers plus a half, that is, halves of odd integers.

The set $H$ of all Hurwitz quaternions can therefore be defined as:
 * $H = \set {a + b \mathbf i + c \mathbf j + d \mathbf k \in \H: \paren {a, b, c, d \in \Z} \text { or } \paren {a, b, c, d \in \Z + \dfrac 1 2} }$

Also see

 * Definition:Lipschitz Quaternion