Herbrand–Ribet theorem
Result on the class group of certain number fields, strengthening Ernst Kummer's theorem / From Wikipedia, the free encyclopedia
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In mathematics, the Herbrand–Ribet theorem is a result on the class group of certain number fields. It is a strengthening of 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 if and only if 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.