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True\False :The ring $\mathbb{Z}_2 \times \mathbb{Z}_2$ is a domain

solution

True A commutative ring with identity is said to be an integral domain if it has no zero divisors.

Eleven-Eleven
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Atish Samraath
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    What is (0,1)(1,0)? – Joshua Mundinger Nov 05 '14 at 02:31
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    $(\bar{1}, \bar{0})(\bar{0},\bar{1}) = (\bar{0}, \bar{0})$. So the ring does have zero-divisors. In fact, an integral domain cannot have a decomposition as $R \times S$, where $R$ and $S$ are non-zero! – SMG Nov 05 '14 at 02:32

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