Timeline for geometric interpretation of "Euclidean domain"
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 17, 2013 at 20:43 | comment | added | Todd Trimble | @ZhenLin Actually, I also got that feeling. But Yazdegerd III's response still seems worthwhile to me. | |
| Oct 17, 2013 at 20:36 | comment | added | Zhen Lin | @ToddTrimble I get the feeling the OP was asking for "geometric" in the sense of $\operatorname{Spec}$. For instance, a reduced ring $A$ is an integral domain if and only if $\operatorname{Spec} A$ is irreducible. | |
| Oct 17, 2013 at 17:26 | comment | added | Todd Trimble | To cement this image, it helps to recall how one typically proves that the Gaussian integers form a Euclidean domain: the key is to show that the ball of radius $1$ (for the algebraic norm on $\mathbb{Q}[i]$) about any point in $\mathbb{Q}[i]$ contains a lattice point in $\mathbb{Z}[i]$, since the furthest you can get from a lattice point is $\sqrt{2}/2$. This really is a thoroughgoingly geometric image, isn't it? | |
| Oct 17, 2013 at 16:58 | history | answered | Name | CC BY-SA 3.0 |