Timeline for Can we make a useful ring on an Elliptic curve? [closed]
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 11, 2011 at 22:43 | comment | added | algori | .. apart from the zero one. | |
| Oct 11, 2011 at 22:32 | comment | added | algori | Joe -- take $G=\mathbb{Q}/\mathbb{Z}$. Since $G\otimes_{\mathbb{Z}}G=0$, there are no ring structures on $G$ at all. | |
| Oct 11, 2011 at 21:24 | history | closed |
Dan Petersen Gjergji Zaimi HJRW Felipe Voloch Zev Chonoles |
not a real question | |
| Oct 11, 2011 at 20:23 | comment | added | Joe Silverman | This question is sufficiently vague as to have little content. First when you say $E$ is an elliptic curve and you want to make $E$ into a ring, you're presumably talking about the points of $E$. So you must specify a field. Second, if you simply want a ring "in a non-trivial way", the answer doesn't seem interesting. (Generally, if $G$ is an abstract abelian group, can one put a non-trivial ring structure on it?) Maybe the right question is: Can we find an algebraic map $E\times E\to E$ that we'll call multiplication and that, with +, satisfies the ring axioms. The answer to that is no. | |
| Oct 11, 2011 at 20:17 | comment | added | user2035 | Not in a useful way, no. Depending on your precise setting (ground field), sometimes not at all. | |
| Oct 11, 2011 at 20:09 | history | asked | Aleks Vlasev | CC BY-SA 3.0 |