"Herbrand-Ribet theorem" meaning in English

{
  "etymology_text": "Named after Jacques Herbrand and Kenneth Ribet.",
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        "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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          "number field",
          "number field"
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          "cyclotomic field",
          "cyclotomic field"
        ],
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          "roots of unity",
          "root of unity"
        ],
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        ],
        [
          "numerator",
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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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        "Jacques Herbrand",
        "Kenneth Ribet"
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  "word": "Herbrand-Ribet theorem"
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{
  "etymology_text": "Named after Jacques Herbrand and Kenneth Ribet.",
  "forms": [
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        "canonical"
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        "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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        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "Jacques Herbrand",
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  "word": "Herbrand-Ribet theorem"
}