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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

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