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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