Timeline for The definitions of a generator module?
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Sep 12, 2016 at 15:10 | history | edited | Jeremy Rickard | CC BY-SA 3.0 |
minor typo
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| Sep 12, 2016 at 11:44 | vote | accept | Xiaosong Peng | ||
| Sep 12, 2016 at 9:59 | comment | added | Xiaosong Peng | Get it! Thank you very much for your help. | |
| Sep 12, 2016 at 9:54 | comment | added | Jeremy Rickard | @Penson $\gamma(A)$ is the submodule of $G^{(I)}$ generated by $\gamma(1)$, and $\gamma(1)\in G^{(J)}$ for some finite $J$. (The important point is that $A$ is finitely generated as an $A$-module: if a finitely generated module is contained in a direct sum then it is contained in a finite subsum.) | |
| Sep 12, 2016 at 9:49 | comment | added | Xiaosong Peng | @ Jeremy Rickard Since A can be seen as a projective A-module, so we can take a splitting map $\gamma : A \rightarrow G^{(I)}$, but if the index set I is infinite, why the image of $\gamma$ is contained in $G^{(J)}$ for some finite J? | |
| Sep 12, 2016 at 9:23 | history | answered | Jeremy Rickard | CC BY-SA 3.0 |