Timeline for Example of a principal ideal which is properly contained in its relative integral closure
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 20, 2017 at 12:10 | comment | added | Jason Starr | By codimension I really meant the height of the corresponding prime ideal. You are correct that I should localize the ring $R$ at the maximal ideal $\mathfrak{m}$. Since the finitely generated $R$-module $S/R$ is annihilated by $\mathfrak{m}$, for every prime ideal $\mathfrak{p}$ with $\mathfrak{p}\subsetneq \mathfrak{m}$, the localization $R_{\mathfrak{p}}$ equals $S_{\mathfrak{p}}$. Thus $R_{\mathfrak{p}}$ is regular for all prime ideals $\mathfrak{p}R_{\mathfrak{m}}$ of $R_\mathfrak{m}$ except the maximal ideal. | |
| Jan 20, 2017 at 12:07 | vote | accept | Cusp | ||
| Jan 20, 2017 at 11:30 | comment | added | Cusp | Here by codimension did you mean embedding dimension (maximal homogeneous ideal ) minus dim R? | |
| S Jan 20, 2017 at 10:02 | history | answered | Jason Starr | CC BY-SA 3.0 | |
| S Jan 20, 2017 at 10:02 | history | made wiki | Post Made Community Wiki by Jason Starr |