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Revision difference : abelian number field |
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| \begin{defn} |
\begin{defn} |
| An abelian number field is a number field $K$ such that $K/\Rats$ is an abelian extension, i.e. $K/\Rats$ is Galois and $\Gal(K/\Rats)$ is an abelian group. |
An abelian number field is a number field $K$ such that $K/\Rats$ is an abelian extension, i.e. $K/\Rats$ is Galois and $\Gal(K/\Rats)$ is an abelian group. |
| \end{defn} |
\end{defn} |
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| The abelian number fields are classified by the Kronecker-Weber Theorem. |
The abelian number fields are classified by the Kronecker-Weber Theorem. |
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| \begin{defn} |
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| A cyclic number field is an (abelian) number field $K$ such that $K/\Rats$ is a Galois extension and $\Gal(K/\Rats)$ is a finite cyclic group (therefore abelian). |
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| \end{defn} |
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