On Wed, Jul 03, 2013 at 06:47:12AM -0700, Travis Scrimshaw wrote:
> For the category of non-unital rings, how about Rngs? (I'm half joking.)
Actually that joke, for good or bad, is what's already been
implemented in successively Axiom, MuPAD, and Sage :-) They even had
Rigs. And Rgs.
But here we want to go further and remove all other axioms
(associativity, additive inverse, ...) but distributivity.
> Somewhat more serious, GeneralAlgebras/GeneralRings? I think
> overall we should be consistent between rings and algebras.
That would be a plus indeed.
> On the math side of things, doesn't a ring in general has to be
> distributive; if so, then I think (distributive) non-* rings
> should be called *Rings and non-distributive things should be
> MultiplicativeAndAdditiveMagmas (or maybe
> AdditiveAndMultiplicativeMagmas).
Thanks for your input.
> Also do we want/have a category for skew fields (a.k.a. division
> rings)?
sage: Rings().Division()
Category of division rings
sage: Rings().Division().Commutative()
Category of fields
sage: Rings().Division().Finite()
Category of finite fields
:-)
Cheers,
Nicolas
--
Nicolas M. Thiéry "Isil" <nthi...@users.sf.net>
http://Nicolas.Thiery.name/
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