Timeline for Can an intersection of ideals in a Noetherian ring be replaced by a countable intersection?
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 1, 2017 at 20:23 | vote | accept | Neil Epstein | ||
| Apr 1, 2017 at 6:48 | answer | added | YCor | timeline score: 12 | |
| Apr 1, 2017 at 4:40 | comment | added | R. van Dobben de Bruyn | My previous answer was wrong (thanks to @Pace Nielsen for pointing that out). I will leave with the following remark: by Krull's intersection theorem, it suffices to show that for each $n$, there exists some countable intersection landing in $\mathfrak m^n$. Remarkably, this does not immediately follow from the fact that $R/\mathfrak m^n$ is Artinian, because intersections do not behave well with respect to quotients (even finite intersections don't). | |
| Mar 31, 2017 at 17:01 | history | asked | Neil Epstein | CC BY-SA 3.0 |