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Show that $\mathbb{Z}_5 [x]/\langle x^2-2\rangle $ and $\mathbb{Z}_5 [x]/\langle x^2-3\rangle$ are not isomorphic

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    Unless I'm mistaken both $x^2-2$ and $x^2-3$ are irreducible over $\mathbb Z_5[x]$. In particular both rings are isomorphic to the field with $25$ elements.2012-11-19
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    Looking through your questions, it appears that they are all homework questions, but none of them have been marked as such. Please read the FAQ and follow the rules of the site. You should mark homework questions as homework, and you should say something about what you've already tried.2012-11-19

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