> 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!? And {0}
also doesn't count as ring?
That one fixes the convention that 'Ring' in any CAS to mean a
mathematical ring with 1 is another question.
> The question I was raising was about the names we wanted to use for
> "rings" without 0 resp. 1.
Z is also a ring without one, i.e., Ring should inherit from Rng. I
would rather say that Rng is a "ring" that *doesn't claim* the existence
of 1.
Ralf
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 *.
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