#18265: Axioms for semigroups: L,R,J,H-trivial, aperiodic
-------------------------------------+-------------------------------------
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: Travis Scrimshaw
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/nthiery/semigroups/axioms-18265 | 06d9bb4d9a360780586283ab8bd7f72383dbcef5
Dependencies: | Stopgaps:
-------------------------------------+-------------------------------------
Changes (by tscrim):
* reviewer: => Travis Scrimshaw
Comment:
Replying to [comment:18 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 :-)
I'm somewhat leaning towards having the implication for the global
inverse, but considering the category of X-trivial groups is, well,
trivial, I don't feel strongly about this. So if you don't feel like doing
it, then you can set this to a positive review.
> 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.
Yes, I believe this should be on a separate ticket.
--
Ticket URL: <http://trac.sagemath.org/ticket/18265#comment:19>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
--
You received this message because you are subscribed to the Google Groups
"sage-trac" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
To post to this group, send email to [email protected].
Visit this group at https://groups.google.com/group/sage-trac.
For more options, visit https://groups.google.com/d/optout.
