(adsbygoogle = window.adsbygoogle || []).push({}); The problem statement, all variables and given/known data

Prove that [tex]Q[x]/\langle x^2 - 2 \rangle[/tex] is ring-isomorphic to [tex]Q[\sqrt{2}] = \{a + b\sqrt{2} \mid a,b \in Q\}[/tex].

The attempt at a solution

Denote [tex]\langle x^2 - 2 \rangle[/tex] by I. [tex]a_0 + a_1x + \cdots + a_nx^n + I[/tex] belongs to Q[x]/I. It has n + 1 coefficients which somehow map to a and b. I don't think any injection can do this. I'm stumped. Any hints?

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# Homework Help: A Ring Isomorphism Problem

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