Herbrand-Ribet theorem

Named after Jacques Herbrand and Kenneth Ribet.

the Herbrand-Ribet theorem

1. (mathematics) 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 B_n for some n, 0 < n < p − 1. The Herbrand–Ribet theorem specifies what, in particular, it means when p divides such an B_n.