Given a commutative ring R with a unit, how do you prove that the product of two ideals, I(adsbygoogle = window.adsbygoogle || []).push({}); _{1}and I_{2}, is also an ideal?

The product of course is defined to be {x*y | x in I_{1}, y in I_{2}}, where * is the multiplication in the ring R.

I'm having trouble proving that I_{1}*I_{2}is a group under addition.

Thanks,

Chen

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# Product of Ideals

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