Timeline for Simple proof that $(p_1x_1-q_1y_1,...,p_nx_n-q_ny_n)$ is a prime ideal
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 31, 2015 at 4:03 | answer | added | Todd Leason | timeline score: 5 | |
| Oct 31, 2015 at 2:34 | comment | added | Todd Leason | @David: Sure, but how to see that the kernel isn't larger ? | |
| Oct 31, 2015 at 2:19 | comment | added | David E Speyer | Seconding Qiaochu, you want to show that this is ideal is the kernel of the map $\mathbb{Z}[x_1, \ldots, x_n, y_1, \ldots, y_n] \to \mathbb{Q}[t_1, \ldots, t_n]$ sending $x_i \to t_i/p_i$, $y_i \to t_i/q_i$. | |
| Oct 31, 2015 at 1:26 | comment | added | Qiaochu Yuan | You want to show that the quotient is an integral domain. It embeds into $\mathbb{Q}[x_1, x_2, \dots x_n]$. | |
| Oct 31, 2015 at 1:19 | history | asked | Todd Leason | CC BY-SA 3.0 |