# Ring isomorphism

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• October 12th 2010, 01:30 PM
AlexanderW
Ring isomorphism
Hello,

the ring of gaussian integers $\mathbb Z[i]$ is isomorphic to the ring $\mathbb Z[x]/(x^2+1)$.

Using this fact, why are the rings $\mathbb Z[i]/p \mathbb Z[i]$ and $\mathbb F_p[x]/(x^2+1)\mathbb F_p[x]$ isomorphic?

Thanks in advance,

Alexander