- #1

silvermane

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## Homework Statement

Prove that if we have two commutative rings R and S and form the product R X S, then R X S cannot be an integral domain.

## The Attempt at a Solution

We have that an integral domain is a commutative ring with 1 not= 0 and with non-zero zero-divisors.

==> (1,0)X(0,1) = (0,0), Thus it's not an integral domain.

I just want to make sure I'm doing this logically correct :)