"Herbrand-Ribet theorem" meaning in All languages combined

{
  "etymology_text": "Named after Jacques Herbrand and Kenneth Ribet.",
  "forms": [
    {
      "form": "the Herbrand-Ribet theorem",
      "tags": [
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  "lang_code": "en",
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      "glosses": [
        "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."
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        [
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        [
          "Bernoulli number",
          "Bernoulli number"
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      "raw_glosses": [
        "(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 Bₙ for some n, 0 < n < p − 1. The Herbrand–Ribet theorem specifies what, in particular, it means when p divides such an Bₙ."
      ],
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        "sciences"
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      "wikipedia": [
        "Jacques Herbrand",
        "Kenneth Ribet"
      ]
    }
  ],
  "word": "Herbrand-Ribet theorem"
}

{
  "etymology_text": "Named after Jacques Herbrand and Kenneth Ribet.",
  "forms": [
    {
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      "tags": [
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      "glosses": [
        "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."
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      "raw_glosses": [
        "(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 Bₙ for some n, 0 < n < p − 1. The Herbrand–Ribet theorem specifies what, in particular, it means when p divides such an Bₙ."
      ],
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      "wikipedia": [
        "Jacques Herbrand",
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  "word": "Herbrand-Ribet theorem"
}