On Tue, May 26, 2009 at 10:21:58AM +0200, Ralf Hemmecke wrote:
>
> > On Sun, May 24, 2009 at 01:44:40PM +0100, John Cremona wrote:
> >> I also would not use "ring" unless it had both a 0 and a 1.
>
> > Sorry, if I was unclearn. I was not doubting the a consensus about this.
>
> Aha, A := 3Z (all multiples of 3) is not a (mathematical) ring!?
> That one fixes the convention that 'Ring' in any CAS to mean a
> mathematical ring with 1 is another question.
That indeed is the scope of the discussion (and btw is also the
default convention for rings in Wikipedia).
> Z is also a ring without one, i.e., Ring should inherit from Rng.
Definitely. And this is the case.
> I would rather say that Rng is a "ring" that *doesn't claim* the
> existence of 1.
Yup, it's like non-associative rings of which rings are a special case.
Now, I need a better name than RingsThatDoNotClaimExistenceOfOne().
> PS: Nicolas, can you give an example of a Rg. I always thought that a
> ring is a commutative group wrt + and a semigroup wrt *.
Well, one can certainly cook up an example. Whether we want to give it
a name that is related to the ring concept is an other question.
Cheers,
Nicolas
--
Nicolas M. Thiéry "Isil" <[email protected]>
http://Nicolas.Thiery.name/
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