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Possible Duplicate:
Comaximal ideals in a commutative ring

Let $I$ and $J$ are coprime ideals in commutative unit ring $A$. Is it true that $I^m$ and $J^n$ are also coprime for any $m,n\in\mathbb{N}$?

Thanks a lot!

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    @pritam Is coprime ideal a synonim for comaximal ideal? It [does not look so](http://planetmath.org/Comaximal.html).2012-10-03
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    @Sasha: According to Atiyah-Macdonald (page 7), yes they are same2012-10-03

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