# Chinese remainder theorem

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Suppose $I_1, I_2, \ldots, I_n$ are ideals in a commutative unital ring $A$, with the property that any two of them are comaximal; in other words, $I_r + I_s = A$ for $r \ne s$. Then the natural map below is an isomorphism:
$A/(I_1I_2 \ldots I_n) \to A/I_1 \times A/I_2 \times \ldots A/I_n$
$I_1I_2\ldots I_n = I_1 \cap I_2 \cap \ldots \cap I_n$