Hi,

On Wed, Jul 03, 2013 at 08:43:06PM +0000, Simon King wrote:
> What I'd prefer is very simple: Just say "algebra" to an algebra. If
> any additional axiom holds, then the algebra should be called
> commutative, associative, unital, noetherian, lie, finite-dimensional,
> or whatever you like. But don't mention the *absence* of axioms!

+1 for this proposal. I think this is not the role of Sage to change
existing mathematical notations/definitions.

In Lang, Algebra (3rd ed., page 121), it is stated that the restriction
to associative and unital algebras is made for the book only.

It is a pity that the name is already used for a more restrictive
notion, but i think that this backward incompatible change is better
that the other currently proposed solutions. Perhaps could we list and
fix all similar misnamings or annoyances during a change of major
version (e.g. Sage 6.0) and announce this clearly, so that we will
suffer only once ?

Ciao,
Thierry

> The only problem is that this very simple solution is backward
> incompatible, because unfortunately Algebras() returns the category of
> *associative* *unital* algebras, in Sage. That's bad. And we would not want
> to deprecate the "Algebras()" command: Not the command itself should be
> deprecated, but its current semantic should be deprecated. So, how could a
> smooth transition be obtained?
> 
> Best regards,
> Simon
> 
> 
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