# Does intersection equal product for infinitely many comaximal ideals?

If $I_1,...,I_n$ are comaximal ideals in a commutative ring, then $I_1\cdots I_n=I_1\cap \cdots \cap I_n$. Does this extend to infinitely many comaximal ideals? The proof I have seen uses induction, so not sure if this does extend.

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How do you define an infinite product of ideals? –  Dylan Moreland Dec 20 '11 at 4:30