Is there a characterisation of those commutative local not necessarily noetherian rings that satisfy Krull's intersection theorem ? How can the intersection theorem be phrased in terms the module category of the ring or its completion ?
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$\begingroup$ Wouldn't it just mean that $R\to \hat{R}$ is injective? $\endgroup$– Donu ArapuraCommented Sep 9, 2011 at 16:17
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$\begingroup$ Or the given ring $R$ is Hausdorff in the $M$-adic topology (where $M$ is its maximal ideal). $\endgroup$– Jesse ElliottCommented Sep 9, 2011 at 18:10
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$\begingroup$ Someone should retag this, but I don't want to bump it to the top and it's not clear to me which tags are appropriate. $\endgroup$– David WhiteCommented Sep 9, 2011 at 20:08
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