7 Oct
2009
7 Oct
'09
8:44 p.m.
Daniel Fischer wrote:
Am Mittwoch 07 Oktober 2009 23:51:54 schrieb Joe Fredette:
I generally find semirings defined as a ring structure without additive inverse and with 0-annihilation (which one has to assume in the case of SRs, I included it in my previous definition because I wasn't sure if I could prove it via the axioms, I think it's possible, but I don't recall the proof).
0*x = (0+0)*x = 0*x + 0*x ==> 0*x = 0
This proof only works if your additive monoid is cancellative, which
need not be true in a semiring. The natural numbers extended with
infinity is one example (if you don't take 0*x = 0 as an axiom, I think
there are two possibilities for 0*∞).
--
Jason McCarty