"ordered field" meaning in All languages combined

{
  "forms": [
    {
      "form": "ordered fields",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "ordered field (plural ordered fields)",
      "name": "en-noun"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "English entries with incorrect language header",
          "parents": [
            "Entries with incorrect language header",
            "Entry maintenance"
          ],
          "source": "w"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Algebra",
          "orig": "en:Algebra",
          "parents": [
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "glosses": [
        "A field which has an order relation satisfying these properties: trichotomy, transitivity, preservation of an inequality when the same element is added to both sides, and preservation of an inequality when the same strictly positive element is multiplied to both sides."
      ],
      "hypernyms": [
        {
          "word": "field"
        },
        {
          "word": "ordered integral domain"
        }
      ],
      "hyponyms": [
        {
          "sense": "Archimedean ordered field",
          "word": "real number system"
        },
        {
          "word": "Euclidean field"
        }
      ],
      "id": "en-ordered_field-en-noun-uHb1zqTJ",
      "links": [
        [
          "algebra",
          "algebra"
        ],
        [
          "field",
          "field"
        ],
        [
          "order relation",
          "order relation"
        ],
        [
          "trichotomy",
          "trichotomy"
        ],
        [
          "transitivity",
          "transitivity"
        ]
      ],
      "raw_glosses": [
        "(algebra) A field which has an order relation satisfying these properties: trichotomy, transitivity, preservation of an inequality when the same element is added to both sides, and preservation of an inequality when the same strictly positive element is multiplied to both sides."
      ],
      "topics": [
        "algebra",
        "mathematics",
        "sciences"
      ],
      "translations": [
        {
          "code": "pt",
          "lang": "Portuguese",
          "sense": "field satisfying the properties of trichotomy, transitivity and preservation of an inequality when the same element is added to both sides",
          "tags": [
            "masculine"
          ],
          "word": "corpo ordenado"
        },
        {
          "code": "ro",
          "lang": "Romanian",
          "sense": "field satisfying the properties of trichotomy, transitivity and preservation of an inequality when the same element is added to both sides",
          "tags": [
            "neuter"
          ],
          "word": "corp ordonat"
        }
      ]
    }
  ],
  "word": "ordered field"
}

{
  "forms": [
    {
      "form": "ordered fields",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "ordered field (plural ordered fields)",
      "name": "en-noun"
    }
  ],
  "hypernyms": [
    {
      "word": "field"
    },
    {
      "word": "ordered integral domain"
    }
  ],
  "hyponyms": [
    {
      "sense": "Archimedean ordered field",
      "word": "real number system"
    },
    {
      "word": "Euclidean field"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "pos": "noun",
  "senses": [
    {
      "categories": [
        "English countable nouns",
        "English entries with incorrect language header",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "en:Algebra"
      ],
      "glosses": [
        "A field which has an order relation satisfying these properties: trichotomy, transitivity, preservation of an inequality when the same element is added to both sides, and preservation of an inequality when the same strictly positive element is multiplied to both sides."
      ],
      "links": [
        [
          "algebra",
          "algebra"
        ],
        [
          "field",
          "field"
        ],
        [
          "order relation",
          "order relation"
        ],
        [
          "trichotomy",
          "trichotomy"
        ],
        [
          "transitivity",
          "transitivity"
        ]
      ],
      "raw_glosses": [
        "(algebra) A field which has an order relation satisfying these properties: trichotomy, transitivity, preservation of an inequality when the same element is added to both sides, and preservation of an inequality when the same strictly positive element is multiplied to both sides."
      ],
      "topics": [
        "algebra",
        "mathematics",
        "sciences"
      ]
    }
  ],
  "translations": [
    {
      "code": "pt",
      "lang": "Portuguese",
      "sense": "field satisfying the properties of trichotomy, transitivity and preservation of an inequality when the same element is added to both sides",
      "tags": [
        "masculine"
      ],
      "word": "corpo ordenado"
    },
    {
      "code": "ro",
      "lang": "Romanian",
      "sense": "field satisfying the properties of trichotomy, transitivity and preservation of an inequality when the same element is added to both sides",
      "tags": [
        "neuter"
      ],
      "word": "corp ordonat"
    }
  ],
  "word": "ordered field"
}