"ordered integral domain" meaning in All languages combined

{
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    {
      "form": "ordered integral domains",
      "tags": [
        "plural"
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      "expansion": "ordered integral domain (plural ordered integral domains)",
      "name": "en-noun"
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  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
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      "glosses": [
        "An integral domain which has a subset whose elements are said to be \"positive\", such that this subset is closed under addition, closed under multiplication, and all elements of the integral domain satisfy a law of trichotomy; namely, that either that element is in the said subset, or it is the zero (additive identity), or its product with −1 (the additive inverse of the multiplicative identity) belongs to the said subset."
      ],
      "hyponyms": [
        {
          "word": "ordered field"
        }
      ],
      "id": "en-ordered_integral_domain-en-noun-sLv1Sbsv",
      "links": [
        [
          "algebra",
          "algebra"
        ],
        [
          "integral domain",
          "integral domain"
        ],
        [
          "trichotomy",
          "trichotomy"
        ]
      ],
      "raw_glosses": [
        "(algebra) An integral domain which has a subset whose elements are said to be \"positive\", such that this subset is closed under addition, closed under multiplication, and all elements of the integral domain satisfy a law of trichotomy; namely, that either that element is in the said subset, or it is the zero (additive identity), or its product with −1 (the additive inverse of the multiplicative identity) belongs to the said subset."
      ],
      "topics": [
        "algebra",
        "mathematics",
        "sciences"
      ]
    }
  ],
  "word": "ordered integral domain"
}

{
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    {
      "form": "ordered integral domains",
      "tags": [
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      "word": "ordered field"
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  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
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      "glosses": [
        "An integral domain which has a subset whose elements are said to be \"positive\", such that this subset is closed under addition, closed under multiplication, and all elements of the integral domain satisfy a law of trichotomy; namely, that either that element is in the said subset, or it is the zero (additive identity), or its product with −1 (the additive inverse of the multiplicative identity) belongs to the said subset."
      ],
      "links": [
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          "algebra",
          "algebra"
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          "integral domain",
          "integral domain"
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          "trichotomy"
        ]
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      "raw_glosses": [
        "(algebra) An integral domain which has a subset whose elements are said to be \"positive\", such that this subset is closed under addition, closed under multiplication, and all elements of the integral domain satisfy a law of trichotomy; namely, that either that element is in the said subset, or it is the zero (additive identity), or its product with −1 (the additive inverse of the multiplicative identity) belongs to the said subset."
      ],
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        "algebra",
        "mathematics",
        "sciences"
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    }
  ],
  "word": "ordered integral domain"
}