Timeline for Correspondence between submodules and quotient modules
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 12, 2013 at 17:44 | vote | accept | GA316 | ||
| Apr 12, 2013 at 17:24 | answer | added | Steven Landsburg | timeline score: 0 | |
| Apr 12, 2013 at 14:04 | comment | added | Andreas Blass | It's not true in general that non-isomorphic submodules give non-isomorphic quotients. For example, in the abelian group (i.e., $\mathbb Z$-module) $(\mathbb Z/4)\times(\mathbb Z/2)$, the cyclic subgroup $(\mathbb Z/4)\times0$ and the non-cyclic subgroup $(2\mathbb Z/4)\times(\mathbb Z/2)$ both produce quotients that are cyclic of order 2. | |
| Apr 12, 2013 at 13:43 | comment | added | GA316 | My intuitive guess is also this same correspondence. but I could not prove that non isomorphic sub modules have non isomorphic quotient modules.. is this very obvious? thanks. | |
| Apr 12, 2013 at 12:49 | comment | added | name | $(N \subset M) \leftrightarrow (M / N)$ | |
| Apr 12, 2013 at 11:46 | history | asked | GA316 | CC BY-SA 3.0 |