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Let $R = Q[x] / (x^4 - 3x^2+ 6x)$. How can we prove that $x^2 + 1$ is invertible in $R$? How can we prove that $R$ is isomorphic to a direct sum of two fields?

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    We would appreciate it to see some thoughts of your own on this. Also, it is a bit rude to command us to prove it.2012-12-13
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    @SugataAdhya: Please do not use $\Bbb R$ ("blackboard" R) for an abstract ring; $\Bbb R$ denotes *the real numbers*, and obviously we are not working with the real numbers here.2012-12-13
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    I'm sorry. I didn't notice.2012-12-13

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