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How can we prove that if $R$ is a commutative Noetherian ring, $\mathfrak{m} = (a_1,\ldots,a_n)$ is an ideal, then the completion of $R$ at $\mathfrak{m}$ is isomorphic to $R[[x_1,\ldots,x_n]]/(x_1-a_1,\ldots,x_n-a_n)$?

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    You don't lose anything from having your entire question in the title. Not having a clear indication of what the question is about just makes it less likely that the people who might be able to help you will take a look.2011-01-06
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    (It never hurts to make explicit the fact that your rings are commutative!)2011-01-06

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