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?
Is $R = Q[x] / (x^4 - 3x^2+ 6x)$ isomorphic to a direct sum of two fields?
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$\begingroup$
abstract-algebra
polynomials
modules
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5We 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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4@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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1I'm sorry. I didn't notice. – 2012-12-13