"Krull dimension" meaning in English

{
  "etymology_text": "Named for Wolfgang Krull, for his work on the height of finitely generated ideals of noetherian rings. The term dimension is from the correspondence between the geometric dimension of an affine variety and the Krull dimension of its coordinate ring.",
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  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
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      "glosses": [
        "The supremum of the lengths of all chains of prime ideals."
      ],
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          "commutative algebra",
          "commutative algebra"
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          "commutative ring",
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      "qualifier": "commutative algebra",
      "raw_glosses": [
        "(commutative algebra, of a commutative ring) The supremum of the lengths of all chains of prime ideals."
      ],
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        "of a commutative ring"
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        "uncountable"
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  "word": "Krull dimension"
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{
  "etymology_text": "Named for Wolfgang Krull, for his work on the height of finitely generated ideals of noetherian rings. The term dimension is from the correspondence between the geometric dimension of an affine variety and the Krull dimension of its coordinate ring.",
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  "lang_code": "en",
  "pos": "noun",
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      "glosses": [
        "The supremum of the lengths of all chains of prime ideals."
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          "commutative algebra"
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          "commutative ring",
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      "qualifier": "commutative algebra",
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        "(commutative algebra, of a commutative ring) The supremum of the lengths of all chains of prime ideals."
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        "of a commutative ring"
      ],
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        "uncountable"
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        "Wolfgang Krull"
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  "word": "Krull dimension"
}