Timeline for Quotient rings of integral quaternion rings
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 6 at 16:57 | answer | added | John Voight | timeline score: 2 | |
| Apr 4 at 14:49 | comment | added | A. Bailleul | Indeed, thank you all for making this clearer. | |
| Apr 3 at 12:38 | comment | added | Kimball | @DaveBenson or $n=1$! | |
| Apr 3 at 7:07 | comment | added | Dave Benson | In a commutative quotient, you have $i=jk=kj=-i$, so $2i=0$ and hence $2=0$ because $i$ is a unit. So if you want $\mathbb{Z}/n\mathbb{Z}$ as a quotient then $n=2$. | |
| Apr 3 at 1:31 | comment | added | Noam D. Elkies | As you can see from the example of the ideal (2) -- which is even 2-sided -- the index can't be given by a^2 + ... + d^2. Rather it is the square of that norm. One way is to compute the volume of the parallelepiped (which in this case is a hypercube) formed by the multiples of your generator by 1,i,j,k. | |
| Apr 2 at 23:59 | history | asked | A. Bailleul | CC BY-SA 4.0 |