Timeline for Rings all of whose torsion modules are cyclic
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 10, 2015 at 20:09 | answer | added | user91132 | timeline score: 2 | |
| Nov 6, 2015 at 3:00 | answer | added | David Handelman | timeline score: 2 | |
| Nov 5, 2015 at 1:50 | comment | added | Qiaochu Yuan | Such a ring $R$ is necessarily noncommutative. Certainly $R$ cannot be a field. If $R$ is commutative it has a nontrivial maximal ideal $m$, and the finitely generated torsion module $R/m \oplus R/m$ is not cyclic because it has dimension $2$ as an $R/m$-vector space. This argument shows more generally that such a ring $R$ cannot admit a nonzero map into a commutative ring. | |
| Nov 5, 2015 at 1:37 | history | asked | Dr. Evil | CC BY-SA 3.0 |