abelian number field

Definition 1.

An abelian number field is a number field $K$ such that $K/\\mathbb{Q}$ is an abelian extension, i.e. $K/\\mathbb{Q}$ is Galois and $\\operatorname{Gal}(K/\\mathbb{Q})$ is an abelian group.

The abelian number fields are classified by the Kronecker-Weber Theorem.

Definition 2.

A cyclic number field is an (abelian) number field $K$ such that $K/\\mathbb{Q}$ is a Galois extension and $\\operatorname{Gal}(K/\\mathbb{Q})$ is a finite cyclic group (therefore abelian).

单词	AbelianNumberField
释义	abelian number field Definition 1. An abelian number field is a number field $K$ such that $K/\\mathbb{Q}$ is an abelian extension, i.e. $K/\\mathbb{Q}$ is Galois and $\\operatorname{Gal}(K/\\mathbb{Q})$ is an abelian group. The abelian number fields are classified by the Kronecker-Weber Theorem. Definition 2. A cyclic number field is an (abelian) number field $K$ such that $K/\\mathbb{Q}$ is a Galois extension and $\\operatorname{Gal}(K/\\mathbb{Q})$ is a finite cyclic group (therefore abelian).
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