Quaternion integers are quaternions whose components take on discrete values
such as integers . . . . . . .

There are several kinds of quaternion integers:

Hurwitz quaternion (or Hurwitz integer) is a quaternion whose components are
either all integers or all half-integers (a mixture of integers and
half-integers is not allowed). The norm of a Hurwitz quaternion, given by
a^2 + b^2 + c^2 + d^2, is always an integer.

A Lipschitz quaternion (or Lipschitz integer) is a quaternion whose
components are all integers.

### Internet references

Wikipedia:
Hurwitz quaternion

Mathworld:
Quaternion

Fact archive:
Quaternion

### Related pages in this website

Complex numbers

The webmaster and author of this Math Help site is
Graeme McRae.