Definition:Lipschitz Quaternion

Definition
A Lipschitz quaternion is a quaternion whose components are all integers.

The set $\Bbb L$ of all Lipschitz quaternions can therefore be defined as:
 * $\Bbb L = \set {a + b \mathbf i + c \mathbf j + d \mathbf k \in \H: a, b, c, d \in \Z}$

Also see

 * Definition:Gaussian Integer
 * Definition:Hurwitz Quaternion