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 <jmcca...@sent.com> _______________________________________________ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe