What is $\mathbb{Z_2^2}$?
Is it the Cartesian product $\mathbb{Z} \times \mathbb{Z}$?
Is it isomorphic to $\mathbb{F}_{4}$?
2026-03-28 13:20:36.1774704036
What is $\mathbb{Z_2^2}$?
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No, it's the Cartesian product $\mathbb{Z}_2\times\mathbb{Z}_2$, where $ \mathbb{Z}_2 $ is the finite field with two elements. However, $\mathbb{Z}_2\times\mathbb{Z}_2$ isn't a field under the induced operations, as $(0,1)$ and $(1,0)$ have no multiplicative inverse.