Timeline for Structure theorem of f.g. modules over a (non) PID
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 14, 2022 at 9:10 | comment | added | Martin Sleziak | The link seems to be dead - and I found it neither in the Wayback Machine nor on the Pierre-Yves Gaillard's new site. Perhaps somebody else might have better luck finding it... | |
| Nov 17, 2010 at 15:08 | comment | added | darij grinberg | Sorry, Pierre, but I don't understand f(x, y) divides f(x, v) in the proof of Proposition 2. What does "maximal" mean - bigger than all, or not smaller than any? And something (which I would call experience, had I any in this field of algebra) makes me seriously doubt that a proof of this result fits in a page... | |
| Nov 16, 2010 at 16:06 | comment | added | Keenan Kidwell | A related question I asked a while back (where somebody also linked to the above pdf) is mathoverflow.net/questions/22722/… For principal artin local rings (like $\mathbb{Z}/p^n\mathbb{Z}$ for a prime $p$ and $n\geq 1$), every element is either a unit or nilpotent, and the structure theorem holds and one has uniqueness. | |
| Nov 16, 2010 at 15:16 | comment | added | Timothy Wagner | According to theorems 7.3,7.5 in Lang's Algebra, the decomposition is unique. | |
| Nov 16, 2010 at 14:46 | comment | added | HenrikRüping | the upper PDF only claims/shows the existence part of the structure theorem. So I guess one can look for a Principal ideal ring with zero divisors, where the uniqueness part fails. | |
| Nov 16, 2010 at 14:44 | history | edited | Timothy Wagner | CC BY-SA 2.5 |
deleted 29 characters in body
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| Nov 16, 2010 at 14:34 | history | answered | Timothy Wagner | CC BY-SA 2.5 |