Timeline for Structure theorem for Finitely Generated modules over PID's using localization
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 29, 2012 at 4:12 | comment | added | Mahdi Majidi-Zolbanin | @Dinesh: I was referring to my own suggested approach, not the whole plan. | |
| Feb 29, 2012 at 2:45 | comment | added | Dinesh | @Martin Brandenburg Can you please elaborate your comments? Is the whole plan naive? | |
| Feb 28, 2012 at 20:30 | comment | added | Mahdi Majidi-Zolbanin | I agree with Martin, it wont work like this. | |
| Feb 28, 2012 at 19:13 | comment | added | Martin Brandenburg | I think this approach is too naive, and you don't get some torsion-free quotient for free ... | |
| Feb 28, 2012 at 17:02 | comment | added | Mahdi Majidi-Zolbanin | @Dinesh: I think it suffices to show $E/E^\prime$ is torsion-free. You can choose the generator of $E^\prime$ to be one of the elements of a minimal set of generators of $E$. That way $E/E^\prime$ can be generated with one less than number of generators of $E$. | |
| Feb 28, 2012 at 16:45 | comment | added | Dinesh | @Mahdi Majidi-Zolbanin So if we can prove $E/E'$ is torsion free with lesser generators than the minimal no.of generators of $E$ then we are done. Right? | |
| Feb 28, 2012 at 16:14 | comment | added | Mahdi Majidi-Zolbanin | Why don't you take a sub-module $E^\prime$ of $E$ generated by a nonzero element of $E$? Since $E$ is torsion-free, such an $E^\prime$ is isomorphic to $R$, so that $S^{-1}E^\prime\cong K$, and you can use induction, using $E^\prime$ and $E/E^\prime$. | |
| Feb 28, 2012 at 13:46 | history | asked | Dinesh | CC BY-SA 3.0 |