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Results tagged with class-field-theory
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user 5513
10
votes
Where does the principal ideal theorem (from CFT) go?
There is a generalization of the principal ideal theorem to ray class groups:
Let $K$ be a number field, $\mathfrak{m}$ a modulus for $K$, $L:=K(\mathfrak{m})$ the ray class field modulo $\mathfrak{ …
- 4,790
4
votes
Fields whose embeddings into the complex numbers are invariant under complex conjugation
The only fields with this property are algebraic over $\mathbb{Q}$. They are either totally real or a quadratic imaginary extension of a totally real field (but not necessarily finite).
Proof: Note t …
- 4,790