Timeline for Simultaneous extension of modules
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 31, 2016 at 12:03 | vote | accept | Dejan Govc | ||
| Oct 15, 2016 at 12:54 | answer | added | Dejan Govc | timeline score: 0 | |
| Jun 29, 2016 at 18:31 | history | edited | Dejan Govc | CC BY-SA 3.0 |
added 253 characters in body
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| Jun 29, 2016 at 18:03 | comment | added | Dejan Govc | @JasonStarr: Thanks, this is certainly useful information. Do you perhaps know of any sufficient conditions on $R$ under which the claim holds? (Aside from $R$ being a field?) | |
| Jun 29, 2016 at 17:36 | comment | added | Jason Starr | That is not true. Let $C$ be a projective $R$-module, and let $B\subset C$ be an $R$-submodule that is not projective, e.g., $C=R=\mathbb{Z}[t]$ and $B=\langle 2,t \rangle$. Let $A\to B$ a surjection from a projective $R$-module. If such a diagram exists, then the middle column would split ($C$ is projective), implying the first column splits, implying that $B$ is projective. | |
| Jun 29, 2016 at 17:25 | history | asked | Dejan Govc | CC BY-SA 3.0 |