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Given a commutative ring R with a unit, how do you prove that the product of two ideals, I_{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
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