Timeline for Classification of symtrivial modules over a PID
Current License: CC BY-SA 3.0
16 events
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| Jan 7, 2014 at 19:56 | history | edited | Will Sawin | CC BY-SA 3.0 |
Reorganized everything
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| Jan 29, 2013 at 0:13 | comment | added | Martin Brandenburg | Alternatively: Finitely generated submodules of $K$ are torsionfree, hence flat, and therefore the property symtrivial descends. | |
| Jan 27, 2013 at 19:55 | comment | added | Will Sawin | yes, because every pair of elements is contained in a symtrivial submodule, that being the fractional ideal generated by those two elements, which is a line bundle, hence symtrivial. | |
| Jan 27, 2013 at 19:09 | comment | added | tj_ | @Will: Is each submodule of $K$ symtrivial ? | |
| Jan 26, 2013 at 10:31 | vote | accept | Martin Brandenburg | ||
| Jan 26, 2013 at 0:55 | comment | added | Will Sawin | (5) Because then $p^{n-1}M/p^nM= p^{n-1}(R/p^kR)=0$. (Q2) Because for each prime $p$, either $F$ is $p$-divisble or $T$ has no $p$-torsion | |
| Jan 25, 2013 at 23:41 | comment | added | Martin Brandenburg | (5) Yes, but how can we exclude $R/p^k R \cong M/p^n M$ for $k<n$? (Q2) Why is there some $y$ such that $ny \equiv x$ mod $T$? This is only clear when $M/T = K$. | |
| Jan 25, 2013 at 21:23 | history | edited | Will Sawin | CC BY-SA 3.0 |
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| Jan 25, 2013 at 19:17 | comment | added | Will Sawin | The kernel is a submodule of $R/p^nR$, which is a quotient of a local ring of a Dedekind domain, hence a DVR, so all ideals are powers of the maximal ideal, $p$. | |
| Jan 25, 2013 at 14:44 | comment | added | Martin Brandenburg | Thanks a lot for the new version, it is very clear. I still have some problems with (5). I see that $R/p^n R \to M/p^n M$ is surjective, but why is it injective? | |
| Jan 25, 2013 at 14:43 | history | edited | Martin Brandenburg | CC BY-SA 3.0 |
minor typos, and completed the proof of (4)
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| Jan 25, 2013 at 3:16 | history | edited | Will Sawin | CC BY-SA 3.0 |
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| Jan 25, 2013 at 0:42 | history | edited | Will Sawin | CC BY-SA 3.0 |
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| Jan 25, 2013 at 0:24 | history | edited | Will Sawin | CC BY-SA 3.0 |
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| Jan 23, 2013 at 22:52 | history | edited | Will Sawin | CC BY-SA 3.0 |
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| Jan 23, 2013 at 22:39 | history | answered | Will Sawin | CC BY-SA 3.0 |