Find the necessary and sufficient condition on integers $D_1,D_2$ for fields $\mathbb{Q}(\sqrt{D_1})$ to be isomorphic to $\mathbb{Q}(\sqrt{D_2})$
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Find the necessary and sufficient condition for $\mathbb{Q}(\sqrt{D_1})$ to be isomorphic to $\mathbb{Q}(\sqrt{D_2})$
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abstract-algebra
ring-theory
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0what do you mean for two square roots to be isomorphic? – 2017-02-02
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0what is $\sqrt{D_1}$? – 2017-02-02
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Theorem: Let be $k$ is a field and $\alpha,\beta$ algebraic over $k$ ,then the map $f:k(\alpha)\to k(\beta)$ is isomorphism if and only if $a,b$ Conjugate element ((i.e roots to same polynomial)).