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Nov 28, 2016 at 18:39 comment added Francesco Polizzi The dual statement is used in the First Uniqueness Theorem. For the Second Uniqueness Theorem, it is used the standard form of the result (see Atiyah-Macdonald, computation just before Theorem 4.10).
Nov 28, 2016 at 18:28 comment added Xam I think you are referring to the "dual" statement: if $I_{1}\cap \ldots \cap I_{n}\subseteq P$ for some prime ideal $P$, then there is $j$ such that $I_{j}\subseteq P$.
Nov 28, 2016 at 18:18 history answered Francesco Polizzi CC BY-SA 3.0