Integers are of course used in calculations involving complex numbers. But are integers ever used in calculations involving quaternions, octonions, etc.? In essence, are integers ever used in complex-valued systems that don't commute?
For extra credit, are there applications that we can list where integers are used with these hypercomplex numbers?
** EDIT **
I'm really just looking for applications that involve quaternions, octonions, etc. and that use integer values instead of real values for each element. I really can't seem to find any, so I'm hoping that someone can list some.