Suppose I have two Galois extensions $F_1, F_2$ of $\mathbb{Q}$ such that $F_1$ has a real embedding. Then is there a general condition on $F_2$ such that $F_1$ and $F_2$ will be linearly disjoint (for example I think if $F_2$ is imaginary quadratic they will be linearly disjoint)?
Real embeddings and linear disjointness
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field-theory
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2Couldn't $F_1$ even be a subfield of $F_2$? For instance, $\Bbb Q(\sqrt{2})$ and $\Bbb Q(\sqrt{2},i)$. – 2012-09-10
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0ah ok, I have edited the question – 2012-09-10