Talk:Totally real number field
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what is an image in this context? Can we have a real world example or analogy?
Galois?
[edit]Is a totally real field always Galois over Q? The typical example for a non-Galois field that comes to my mind is Q(n-th root of 2), n>2 , which is not totally real. --Roentgenium111 (talk) 20:57, 19 March 2009 (UTC)
- No, just find an irreducible cubic polynomial f with real roots but whose Galois group is S3, so the splitting field of f will have degree 6, but adjoining one of its roots to Q will give a field of degree 3. An example of such a polynomial is f(X) = X3 − 4X+1. Chenxlee (talk) 13:35, 25 March 2009 (UTC)