Timeline for Can the projective line be provided with a ring structure?
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 2, 2015 at 18:00 | comment | added | Qiaochu Yuan | If $K$ doesn't contain a square root of $-1$, then your group is the quotient of the multiplicative group of $K[i]$ by the multiplicative group of $K$. The closest ring in sight is $K[i]$, which, being a field, has no nontrivial quotients. | |
| Aug 2, 2015 at 17:44 | comment | added | Qiaochu Yuan | Your proposed multiplication isn't well-defined if $K$ itself already contains a square root of $-1$: in this case, $K[i]$ has zero divisors, so it's possible for the "product" of two points to have both coordinates zero and hence to not be a well-defined point on the projective line. | |
| Aug 2, 2015 at 17:29 | vote | accept | Wolfgang Tintemann | ||
| Aug 2, 2015 at 17:10 | answer | added | Qiaochu Yuan | timeline score: 12 | |
| Aug 2, 2015 at 15:54 | answer | added | Ben Webster♦ | timeline score: 9 | |
| Aug 2, 2015 at 15:37 | history | asked | Wolfgang Tintemann | CC BY-SA 3.0 |