## If Two Ideals Are Comaximal in a Commutative Ring, then Their Powers Are Comaximal Ideals

## Problem 360

Let $R$ be a commutative ring and let $I_1$ and $I_2$ be **comaximal ideals**. That is, we have

\[I_1+I_2=R.\]

Then show that for any positive integers $m$ and $n$, the ideals $I_1^m$ and $I_2^n$ are comaximal.

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