19 Dec
2018
19 Dec
'18
10:57 a.m.
I'll save complex radices for another day. And I'm pretty sure that quaternion radices won't work, i.e. can't represent all quaternions given nothing but real integer digits.
Yes, that follows because the R-algebra generated by a single quaternion is isomorphic to R (if it's real) or C (if it's not). There's a similar result for octonions: any pair {x, y} of octonions generates an R-algebra isomorphic to either R, C, or H (depending on whether the dimension of the R-linear span of {1, x, y} is 1, 2, or 3, respectively). Best wishes, Adam P. Goucher