By F[X] I mean the polynomials with coefficients in field F. By F(X) I mean the rational polynomials.(adsbygoogle = window.adsbygoogle || []).push({});

I have a feeling that [itex]\boxed{ \mathbb Q( \sqrt 2 ) \cong \frac{\mathbb Q[X]}{(X^2-2)}} [/itex]. (if not readable: the RHS is with [X])

Is thistrue? If so, how can Iproveit? I suppose it would suffice I could show that the RHS is the smallest field extension of the rationals that contains sqrt(2) (as the LHS is obviously just that).

Also, is there maybe evena more general resultbehind this?

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# Is this correct? Field extension of the rationals

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