#18265: Axioms for semigroups: L,R,J,H-trivial, aperiodic
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Reporter: nthiery | Owner:
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-7.2
Component: algebra | Resolution:
Keywords: | Merged in:
Authors: Nicolas M. Thiéry | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/nthiery/semigroups/axioms-18265 | 06d9bb4d9a360780586283ab8bd7f72383dbcef5
Dependencies: | Stopgaps:
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Comment (by nthiery):
Replying to [comment:16 tscrim]:
> I think we should also add that an inverse R-trivial monoids implies
J/H-trivial.
Yes, but only when we will have the "inverse" axiom in the sense of
local inverses in semigroups. Our current Inverse axiom is about
having a global inverse (it's indeed annoying that we have this naming
conflict, but there is nothing much we can do about it).
Of course an R-trivial monoid with a global inverse is J/H trivial,
but that's not super interesting :-)
> > This would be cute, indeed. I'll have a quick look if it's trivial to
> > do. Otherwise, we can leave it for later; that will be easy to change
> > anyway.
>
> Let me know.
I made a quick fix, so that JTrivial is displayed as j trivial and not
jtrivial; it only slightly better, but requires no special casing and
makes for a more consistent implementation of uncamelcasing.
It's been discussed several times that axioms like AdditiveAssociative
would be better displayed as `additive-associative`, to raise
ambiguities in expressions such as:
{{{
Category of associative additive commutative additive associative
additive unital distributive magmas and additive magmas
}}}
This would make the `j trivial` into `j-trivial` as a by-product
without any special casing. However this is a relatively invasive
change (it will require updating a bunch of doctests"), so I vote for
doing this in a separate ticket.
Do you agree that this is good enough for now?
--
Ticket URL: <http://trac.sagemath.org/ticket/18265#comment:18>
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