17 Oct
2011
17 Oct
'11
7:19 p.m.
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.