On October 17, 2011 19:19:18 Paterson, Ross wrote:
Balazs Komuves writes:
Rings with unity have a canonical map, actually a ring homomorphism (but not necessarily injection) from the integers, namely for the natural integer N, you add together the unit element with itself N times. For negative N, you take the additive inverse.
For fields, you would try to extend this to rationals; however, it seems that because of the non-injectivity of the above, this won't always work. Example: finite fields. In a finite field of order P, we would have f(N/P) = f(N)/f(P) = f(N)/0 which is not defined.
Good point. Mind you we already have this with Ratio Int and friends.
Yes. It doesn't really strike me as such an issue. Really just another statement that "recip zero" is not defined. Cheers! -Tyson PS: Thanks for the info on the canonical map Balazs. Very nice.