Timeline for A $0$-dimensional ring that is not noetherian
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 22, 2018 at 10:23 | comment | added | Armando j18eos | More in general, thisi example works for any field $\mathbb{K}$ instead $\mathbb{Q}$. | |
| Apr 13, 2012 at 12:00 | comment | added | Greg Stevenson | Ah, thanks - my bad... I for some reason was reading $i<j$. | |
| Apr 13, 2012 at 6:41 | comment | added | Mariano Suárez-Álvarez | ...so there is exactly one prime ideal, the one generated by the variables, so that the Krull dimension is zero. | |
| Apr 13, 2012 at 6:35 | comment | added | Mariano Suárez-Álvarez | I am modding out by all products $x_ix_j$ with any $i$ and any $j$. In particular, $x_i^2$ is zero in the quotient. | |
| Apr 13, 2012 at 5:55 | comment | added | Greg Stevenson | Sorry for the dumb question but I am confused - why is this ring zero dimensional? For $i\in \mathbb{N}$ aren't the ideals $(x_j\vert j\neq i)$ prime with quotient $\mathbb{Q}[x_i]$? So this ring would have dimension 1... Even if I made a silly mistake here I don't see how it could be von Neumann regular. | |
| Apr 6, 2012 at 14:26 | comment | added | Georges Elencwajg | Nice example, Mariano. Somehow, I have the feling it is not the last time we are seeing it:) | |
| Apr 6, 2012 at 8:23 | history | answered | Mariano Suárez-Álvarez | CC BY-SA 3.0 |