History of tag 0315
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changed the proof
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2021-07-18 |
70471ab |
Fix error in proof in modules on sites
Thanks to Owen
https://stacks.math.columbia.edu/tag/093M#comment-6266
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changed the proof
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2014-09-20 |
e802cd2 |
Comment about Tag 0315
In the proof of Tag 0315 the ideal I need not need to be nilpotent.
Instead we use that I/I^n is nilpotent in the ring R/I^n. Your
proof is essentially how the proof of Nakayama's lemma in the
nilpotent case works.
I have added a sentence with the explanation.
The reason for not adding your argument is that generally speaking
we try to avoid having the same thing proven in multiple locations,
although in this case your argument is so short that in some sense
it might be quicker to put it in.
On Tue, Sep 16, 2014 at 3:51 PM, Minseon Shin <shinms@berkeley.edu> wrote:
> Hello,
>
> Here is a comment regarding the beginning of the proof of Lemma 10.91.1 (Tag
> 0315). I think the reference to Nakayama's lemma (Lemma 10.18.1, Tag 00DV)
> is sort of confusing here because, unless I am mistaken, it seems to me that
> the claim "M/IM \to N/IN surjective implies M/I^{n}M \to N/I^{n}N surjective
> for all n \ge 1" is true even if M and N are not finitely generated and I is
> not nilpotent. Here is my claimed proof (which is by induction on n):
>
> It is equivalent to say "\phi(M)+IN = N implies \phi(M)+I^{n}N = N for all n
> \ge 1". Suppose \phi(M)+I^{n}N = N. Then I\phi(M)+I^{n+1}N = IN. Adding
> \phi(M) to both sides gives \phi(M)+I^{n+1}N = \phi(M)+(I\phi(M)+I^{n+1}N) =
> \phi(M)+IN = N.
>
> Best,
> Minseon
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changed the statement and the proof
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2010-10-06 |
3b0820b |
Fixing references, etc
Fallout from moving stuff in the previous commit.
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changed the proof
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2010-08-31 |
2e1c8ce |
Constructible subsets of Noetherian spaces
Namely, the characterization in terms of intersections with
irreducible closed subsets.
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changed the proof
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2009-09-29 |
efc115c |
Algebra+Homology: Change to avoid forward references
modified: algebra.tex
modified: homology.tex
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assigned tag 0315
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2009-08-21 |
15d48db
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Added new tags
modified: tags/tags
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changed the label to lemma-completion-generalities
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2009-08-17 |
946301b |
More on comlpetion and towards Nagata rings are universally Japanese
modified: algebra.tex
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changed the statement and the proof
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2009-08-17 |
946301b |
More on comlpetion and towards Nagata rings are universally Japanese
modified: algebra.tex
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created statement with label lemma-ses-completion in algebra.tex
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2009-08-17 |
54b3586 |
More stuff in algebra.tex:
Integral closure is transitive
Surjectivity of completion of surjective maps?
Definition of I-adically complete modules
Criterion as to when completion is complete
Completion complete in Noetherian case
Finiteness criterion (still not done)
Residue field extension of map dvrs bounded
Complete local ring with finitely generated maximal ideal is
Noetherian
Lemmas on Japanese property
Starting to prove Tate's theorem on Japaneseness of complete
rings
modified: algebra.tex
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