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In mathematics, a ray class field is an abelian extension of a global field associated with a ray class group of ideal classes or idele classes. Every finite abelian extension of a number field is contained in one of its ray class fields. There are two slightly different notions of what a ray class field is, as authors differ in how the infinite primes are treated.

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• In mathematics, a ray class field is an abelian extension of a global field associated with a ray class group of ideal classes or idele classes. Every finite abelian extension of a number field is contained in one of its ray class fields. The term "ray class group" is a translation of the German term "Strahlklassengruppe". Here "Strahl" is the German for a ray, and often means the positive real line, which appears in the positivity conditions defining ray class groups. , p.6) uses "Strahl" to mean a certain group of ideals defined using positivity conditions, and uses "Strahlklasse" to mean a coset of this group. There are two slightly different notions of what a ray class field is, as authors differ in how the infinite primes are treated. (en)
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• In mathematics, a ray class field is an abelian extension of a global field associated with a ray class group of ideal classes or idele classes. Every finite abelian extension of a number field is contained in one of its ray class fields. There are two slightly different notions of what a ray class field is, as authors differ in how the infinite primes are treated. (en)
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• Ray class field (en)
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