28 Nov
2013
28 Nov
'13
1:11 p.m.
I don't have my Knuth in front of me, but I think Knuth already talked about the non-commutative case, including matrices of various sorts. Also, doesn't Hurwitz talk about gcd's over his quaternions? At 12:05 PM 11/28/2013, Dan Asimov wrote:
Anyway, I think GCD makes the most sense only in principal ideal domains.
Hmm, I think we've been tacitly assuming the ring is commutative. What if it isn't?
Take for example the ring Li of Lipschitz quaternions := Z + Zi + Zj + Zk.
Or the ring Hu of Hurwitz quaternions := Li[(1+i+j+k)/2].