#11068: Basic implementation of one- and twosided ideals of non-commutative
rings,
and quotients by twosided ideals
-----------------------------------------------------------------+----------
Reporter: SimonKing |
Owner: AlexGhitza
Type: enhancement |
Status: needs_review
Priority: major |
Milestone: sage-4.7.2
Component: algebra |
Keywords: onesided twosided ideal noncommutative ring sd32
Work_issues: multiplication in quotient rings of matrix spaces |
Upstream: N/A
Reviewer: |
Author: Simon King
Merged: |
Dependencies: #10961, #9138, #11115, #11342
-----------------------------------------------------------------+----------
Changes (by SimonKing):
* status: needs_work => needs_review
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
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
Apply all three patches.
--
Comment:
I submitted a third patch, and I think it works now!
We have the new doctest
{{{
sage: MS = MatrixSpace(GF(5),2,2)
sage: I = MS*[MS.0*MS.1,MS.2+MS.3]*MS
sage: Q = MS.quo(I)
sage: Q.lift()
Set-theoretic ring morphism:
From: Quotient of Full MatrixSpace of 2 by 2 dense matrices over Finite
Field of size 5 by the ideal
(
[0 1]
[0 0],
[0 0]
[1 1]
)
To: Full MatrixSpace of 2 by 2 dense matrices over Finite Field of
size 5
Defn: Choice of lifting map
}}}
The tests in sage/rings/ pass (didn't run the other tests yet). Ready for
review again!
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11068#comment:38>
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