#11068: Basic implementation of one- and twosided ideals of non-commutative
rings,
and quotients by twosided ideals
---------------------------+------------------------------------------------
Reporter: SimonKing | Owner: AlexGhitza
Type: enhancement | Status: positive_review
Priority: major | Milestone: sage-4.7.3
Component: algebra | Keywords: onesided twosided ideal
noncommutative ring sd32
Work_issues: | Upstream: N/A
Reviewer: John Perry | Author: Simon King
Merged: | Dependencies: #10961 #9138 #11115 #11342 #11339
---------------------------+------------------------------------------------
Changes (by SimonKing):
* dependencies: #10961 #9138 #11115 #11342 => #10961 #9138 #11115 #11342
#11339
Old description:
> It was suggested that my patch for #7797 be split into several parts.
>
> The first part shall be about ideals in non-commutative rings. Aim, for
> example:
> {{{
> sage: A = SteenrodAlgebra(2)
> sage: A*[A.0,A.1^2]
> Left Ideal (Sq(1), Sq(1,1)) of mod 2 Steenrod algebra
> sage: [A.0,A.1^2]*A
> Right Ideal (Sq(1), Sq(1,1)) of mod 2 Steenrod algebra
> sage: A*[A.0,A.1^2]*A
> Twosided Ideal (Sq(1), Sq(1,1)) of mod 2 Steenrod algebra
> }}}
>
> It was suggested to also add quotients by twosided ideals, although it
> will be difficult to provide examples before having letterplace ideals.
>
> Depends on #10961 #9138 #11115
>
> Apply:
>
> * [attachment:trac11068_nc_ideals_and_quotients.patch]
> * [attachment:trac11068_quotient_ring_without_names.patch]
> * [attachment:trac11068_lifting_map.patch]
New description:
It was suggested that my patch for #7797 be split into several parts.
The first part shall be about ideals in non-commutative rings. Aim, for
example:
{{{
sage: A = SteenrodAlgebra(2)
sage: A*[A.0,A.1^2]
Left Ideal (Sq(1), Sq(1,1)) of mod 2 Steenrod algebra
sage: [A.0,A.1^2]*A
Right Ideal (Sq(1), Sq(1,1)) of mod 2 Steenrod algebra
sage: A*[A.0,A.1^2]*A
Twosided Ideal (Sq(1), Sq(1,1)) of mod 2 Steenrod algebra
}}}
It was suggested to also add quotients by twosided ideals, although it
will be difficult to provide examples before having letterplace ideals.
Depends on #10961 #9138 #11115 #11339
Apply:
* [attachment:trac11068_nc_ideals_and_quotients.patch]
* [attachment:trac11068_quotient_ring_without_names.patch]
* [attachment:trac11068_lifting_map.patch]
--
Comment:
There was a conflict of the first patch with some cosmetical change that
was done at #11339. Since #11339 has a positive review as well, I was
changing the first patch. Since the code did not change (only the line
breaks changed), I keep the positive review, but to be on the safe side
I'll run doc tests now.
Apply trac11068_nc_ideals_and_quotients.patch
trac11068_quotient_ring_without_names.patch trac11068_lifting_map.patch
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11068#comment:56>
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