Timeline for relation between Min(R) and Min(R^)
Current License: CC BY-SA 3.0
3 events
| when toggle format | what | by | license | comment | |
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| May 15, 2012 at 3:12 | comment | added | Mahdi Majidi-Zolbanin | To be more precise, the example in Bourbaki exercises is the following: $K$ is an algebraically closed field of char $0$, $R=K[X,Y]$, $p=X(X^2+Y^2)+(X^2-Y^2)$. Then one can show the ideal $pR$ is prime. So $R/pR$ is a domain. If $\mathfrak{m}$ is the maximal ideal of $R/pR$ generated by $X$ and $Y$, then the exercise asks to show that the $\mathfrak{m}$-adic completion of $R/pR$ is not a domain. The given hint is to show that $p$ decomposes into a product of two formal power series in $K[[X,Y]]$. | |
| May 14, 2012 at 14:48 | vote | accept | Stella | ||
| May 13, 2012 at 2:23 | history | answered | Mahdi Majidi-Zolbanin | CC BY-SA 3.0 |