#17096: Implement categories for filtered algebras
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Reporter: tscrim | Owner: tscrim
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.4
Component: categories | Resolution:
Keywords: filtered algebras | Merged in:
Authors: Travis Scrimshaw | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
public/categories/filtered_algebras-17096|
b29f67e46e18721313330d3a6e116cf3df2eaf8e
Dependencies: | Stopgaps:
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Comment (by jhpalmieri):
A few questions and comments:
- in `filtered_modules.py`, it talks about modules over a commutative
ring, but the word "commutative" can be deleted, I think.
- in the same file, it says
{{{
.. TODO::
Implement a notion for decreasing filtrations: where `F_j \subseteq
F_i`.
}}}
If you want to keep this remark, then you should add "when i \leq j". But
do you need to keep this? If you want a decreasing filtration, just use
the non-positive integers for your indexing set instead of non-negative
integers. For example, if you have an algebra `A` and an ideal `I`, then
you can set `F_{-n}A` equal to the `n`th power of `I`. Then you have `F_0
\supseteq F_{-1} \supseteq F_{-2} \supseteq ...`: a decreasing filtration.
- How could we implement an algebra which is both graded and filtered?
This is the situation for the Steenrod algebra, for example.
--
Ticket URL: <http://trac.sagemath.org/ticket/17096#comment:35>
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