Timeline for Why can't one modify Kaplansky's proof to conclude that every projective module is a direct sum of its finitely generated projetive submodules?
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 22, 2014 at 16:49 | vote | accept | Hua Wang | ||
| Apr 22, 2014 at 16:49 | comment | added | Hua Wang | Ah, I see it now. The stupid mistake I made is that I took condition (4) for granted, while in fact it's not true in general. Thanks a lot. | |
| Apr 22, 2014 at 16:04 | comment | added | Jeremy Rickard | No. The point is that you each time you add an $x_{ij}$, that may not be in either $P$ or $Q$, your current list of elements may not suffice to generate the components of $x_{ij}$ in $P$ and $Q$, so you then have to go on to include more elements to generate these, and then you need to deal with these new elements, and then ... | |
| Apr 22, 2014 at 15:55 | comment | added | Hua Wang | But in this case, I think there's only finitely many rows to be considered, corresponding to a finite generating set of the initial $M_i$. | |
| Apr 22, 2014 at 15:48 | history | answered | Jeremy Rickard | CC BY-SA 3.0 |