In mathematics, a ring class field is the abelian extension of an algebraic number field K associated by class field theory to the ring class group of some order O of the ring of integers of K.[1]

Properties

Let K be an algebraic number field.

Let L be the ring class field for the order Z[n] in the number field K = Q(n).

References

  1. Frey, Gerhard; Lange, Tanja (2006), "Varieties over special fields", Handbook of elliptic and hyperelliptic curve cryptography, Discrete Math. Appl. (Boca Raton), Chapman & Hall/CRC, Boca Raton, Florida, pp. 87–113, MR 2162721. See in particular p. 99.


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