Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

how it is described the normalization of $Spec(k[[x,y]]/(xy))$? In particular call this $N$. Why $N$ can be written as the inersection of 2 local rings and the same holds for the maximal ideal (with 2 maximal ideals)?

share|improve this question
Can you see geometrically what the normalization is? Consider first the non-completed situation, $k[x,y]/(xy)$, make a picture... –  Mariano Suárez-Alvarez Feb 14 '11 at 17:37
@Mariano Suarez-Alvarez is it something like this $k[x]\oplus k[y] $??this is not normal! I have to take $Spec(k[x])\cup Spec(k[y])$ ans normalization –  unknown Feb 15 '11 at 9:26
I do not understand your comment. –  Mariano Suárez-Alvarez Feb 15 '11 at 16:45
@Mariano Suarez-Alvarez geometrically it is easy: 2 disjoint lines. But why can I write it as intersection of 2 local rings? –  unknown Feb 17 '11 at 10:16

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.