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I need help with a problem dealing with completion. It's hard for me to understand how to use the theory for specific examples, so help would be appreciated.

Let $R = \mathbb{C}[x,y,z]/ (zy^2-x^3)$ and let $I=(z)$. Describe the completion ring $\hat{R}^{I}$ and find its maximal ideals.

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Welcome to MSE! Is this homework? If so, please tag it as such. Regards – Amzoti Jan 11 '13 at 22:46
Theorem 8.11 in Matsumura's Commutative Ring Theory might be helpful. – mbrown Jan 11 '13 at 23:14
There is a bijective correspondence between the maximal ideals of $\hat R^I$ and the maximal ideals of $R/I$ and $R/I\simeq\mathbb C[X]/(X^3)[Y]$. – user26857 Jan 12 '13 at 0:49

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