"Abel's irreducibility theorem" meaning in English

{
  "etymology_text": "Described in 1829 by Niels Henrik Abel.",
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  "lang_code": "en",
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      "glosses": [
        "A field theory result asserting that if ƒ(x) is a polynomial over a field F that shares a root with a polynomial g(x) that is irreducible over F, then every root of g(x) is a root of ƒ(x)."
      ],
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          "polynomial",
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        [
          "field",
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        [
          "root",
          "root"
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        [
          "irreducible",
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      "raw_glosses": [
        "(mathematics) A field theory result asserting that if ƒ(x) is a polynomial over a field F that shares a root with a polynomial g(x) that is irreducible over F, then every root of g(x) is a root of ƒ(x)."
      ],
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        "Niels Henrik Abel"
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  "word": "Abel's irreducibility theorem"
}

{
  "etymology_text": "Described in 1829 by Niels Henrik Abel.",
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      "expansion": "Abel's irreducibility theorem",
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      "glosses": [
        "A field theory result asserting that if ƒ(x) is a polynomial over a field F that shares a root with a polynomial g(x) that is irreducible over F, then every root of g(x) is a root of ƒ(x)."
      ],
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          "root",
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      "raw_glosses": [
        "(mathematics) A field theory result asserting that if ƒ(x) is a polynomial over a field F that shares a root with a polynomial g(x) that is irreducible over F, then every root of g(x) is a root of ƒ(x)."
      ],
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        "Niels Henrik Abel"
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  "word": "Abel's irreducibility theorem"
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