Word.ws English Dictionary

Herbrand-Ribet theorem

Herbrand-Ribet theorem proper noun: a result on the class group of certain number fields, strengthening Ernst Kummer's theorem to the effect that the prime p divides the class number of the cyclotomic field of p-th roots of unity iff p divides the numerator of the n-th Bernoulli number Bₙ for some n, 0 < n < p − 1. The Herbrand–Ribet theorem specifies what, in particular, it means when p divides such an Bₙ.

Proper noun

the Herbrand-Ribet theorem

  1. A result on the class group of certain number fields, strengthening Ernst Kummer's theorem to the effect that the prime p divides the class number of the cyclotomic field of p-th roots of unity iff p divides the numerator of the n-th Bernoulli number Bₙ for some n, 0 < n < p − 1. The Herbrand–Ribet theorem specifies what, in particular, it means when p divides such an Bₙ.

Origin of Herbrand-Ribet theorem

Named after Jacques Herbrand and Kenneth Ribet.

Questions about Herbrand-Ribet theorem

What does Herbrand-Ribet theorem mean?
Herbrand-Ribet theorem means a result on the class group of certain number fields, strengthening Ernst Kummer's theorem to the effect that the prime p divides the class number of the cyclotomic field of p-th roots of unity iff p divides the numerator of the n-th Bernoulli number Bₙ for some n, 0 < n < p − 1. The Herbrand–Ribet theorem specifies what, in particular, it means when p divides such an Bₙ.
What part of speech is Herbrand-Ribet theorem?
Herbrand-Ribet theorem is a proper noun.

Words near Herbrand-Ribet theorem in the dictionary

  1. Herbrand function
  2. Herbrand functions
  3. Herbrand universe
  4. Herbrand universes
  5. Herbrand's theorem
  6. Herbrand-Ribet theorem
  7. Herbrandization
  8. Herbrands
  9. herbs
  10. herbs and spices
  11. herbs de Provence

Source and license

Adapted from Wiktionary: Herbrand-Ribet theorem (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

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