"algebraic closure" meaning in All languages combined

{
  "categories": [
    {
      "kind": "other",
      "name": "Locutions nominales en anglais",
      "parents": [],
      "source": "w"
    },
    {
      "kind": "other",
      "name": "Anglais",
      "orig": "anglais",
      "parents": [],
      "source": "w"
    }
  ],
  "forms": [
    {
      "form": "algebraic closures",
      "tags": [
        "plural"
      ]
    }
  ],
  "lang": "Anglais",
  "lang_code": "en",
  "pos": "noun",
  "pos_title": "Locution nominale",
  "related": [
    {
      "word": "algebraically closed"
    }
  ],
  "senses": [
    {
      "categories": [
        {
          "kind": "other",
          "name": "Exemples en anglais",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Exemples en anglais à traduire",
          "parents": [],
          "source": "w"
        },
        {
          "kind": "other",
          "name": "Lexique en anglais de l’algèbre",
          "parents": [],
          "source": "w"
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      ],
      "examples": [
        {
          "bold_text_offsets": [
            [
              26,
              43
            ],
            [
              118,
              135
            ],
            [
              164,
              181
            ],
            [
              321,
              338
            ]
          ],
          "ref": "John Swallow, Exploratory Galois Theory, Cambridge University Press, 2004, page 179",
          "text": "While Complex contains an algebraic closure of ℚ, it is by no means the only algebraically closed field containing an algebraic closure of ℚ. We denote by ℚalg the algebraic closure of ℚ in Complex ; this field is simply the subfield of Complex consisting of algebraic numbers. The field ℚalg is isomorphic, then, to any algebraic closure of ℚ, but even knowing that it is unique up to isomorphism very likely leaves us no more familiar with ℚalg than we were."
        }
      ],
      "glosses": [
        "Clôture algébrique."
      ],
      "id": "fr-algebraic_closure-en-noun-yomA6z7j",
      "topics": [
        "algebra"
      ]
    }
  ],
  "word": "algebraic closure"
}

{
  "categories": [
    "Locutions nominales en anglais",
    "anglais"
  ],
  "forms": [
    {
      "form": "algebraic closures",
      "tags": [
        "plural"
      ]
    }
  ],
  "lang": "Anglais",
  "lang_code": "en",
  "pos": "noun",
  "pos_title": "Locution nominale",
  "related": [
    {
      "word": "algebraically closed"
    }
  ],
  "senses": [
    {
      "categories": [
        "Exemples en anglais",
        "Exemples en anglais à traduire",
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              26,
              43
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              118,
              135
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              164,
              181
            ],
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              321,
              338
            ]
          ],
          "ref": "John Swallow, Exploratory Galois Theory, Cambridge University Press, 2004, page 179",
          "text": "While Complex contains an algebraic closure of ℚ, it is by no means the only algebraically closed field containing an algebraic closure of ℚ. We denote by ℚalg the algebraic closure of ℚ in Complex ; this field is simply the subfield of Complex consisting of algebraic numbers. The field ℚalg is isomorphic, then, to any algebraic closure of ℚ, but even knowing that it is unique up to isomorphism very likely leaves us no more familiar with ℚalg than we were."
        }
      ],
      "glosses": [
        "Clôture algébrique."
      ],
      "topics": [
        "algebra"
      ]
    }
  ],
  "word": "algebraic closure"
}