"field extension" meaning in English

{
  "forms": [
    {
      "form": "field extensions",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "field extension (plural field extensions)",
      "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"
        },
        {
          "kind": "topical",
          "langcode": "en",
          "name": "Algebraic geometry",
          "orig": "en:Algebraic geometry",
          "parents": [
            "Algebra",
            "Geometry",
            "Mathematics",
            "Formal sciences",
            "Sciences",
            "All topics",
            "Fundamental"
          ],
          "source": "w"
        }
      ],
      "examples": [
        {
          "ref": "1974, Thomas W. Hungerford, Algebra, Springer, page 230",
          "text": "A Galois field extension may be defined in terms of its Galois group (Section 2) or in terms of the internal structure of the extension (Section 3).",
          "type": "quotation"
        },
        {
          "text": "1998, David Goss, Basic Structures of Function Field Arithmetic, Springer, Corrected 2nd Printing, page 283,\nNote that the extension of L obtained by adjoining all division points of ψ includes at most a finite constant field extension."
        },
        {
          "text": "2007, Pierre Antoine Grillet, Abstract Algebra, Springer, 2bd Edition, page 530,\nA field extension of a field K is, in particular, a K-algebra. Hence any two field extensions of K have a tensor product that is a K-algebra."
        }
      ],
      "glosses": [
        "Any pair of fields, denoted L/K, such that K is a subfield of L."
      ],
      "hyponyms": [
        {
          "word": "algebraic extension"
        },
        {
          "word": "transcendental extension"
        },
        {
          "word": "simple extension"
        },
        {
          "word": "trivial extension"
        }
      ],
      "id": "en-field_extension-en-noun-sXQSDCq0",
      "links": [
        [
          "algebra",
          "algebra"
        ],
        [
          "algebraic geometry",
          "algebraic geometry"
        ],
        [
          "fields",
          "field#English"
        ],
        [
          "subfield",
          "subfield"
        ]
      ],
      "meronyms": [
        {
          "word": "base field"
        },
        {
          "word": "extension field"
        }
      ],
      "qualifier": "field theory",
      "raw_glosses": [
        "(algebra, field theory, algebraic geometry) Any pair of fields, denoted L/K, such that K is a subfield of L."
      ],
      "related": [
        {
          "word": "extension"
        },
        {
          "word": "extension field"
        }
      ],
      "topics": [
        "algebra",
        "algebraic-geometry",
        "geometry",
        "mathematics",
        "sciences"
      ],
      "translations": [
        {
          "code": "fi",
          "lang": "Finnish",
          "sense": "pair of fields such that one is a subfield of the other",
          "word": "kuntalaajennus"
        }
      ],
      "wikipedia": [
        "field extension"
      ]
    }
  ],
  "word": "field extension"
}

{
  "forms": [
    {
      "form": "field extensions",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "field extension (plural field extensions)",
      "name": "en-noun"
    }
  ],
  "hyponyms": [
    {
      "word": "algebraic extension"
    },
    {
      "word": "transcendental extension"
    },
    {
      "word": "simple extension"
    },
    {
      "word": "trivial extension"
    }
  ],
  "lang": "English",
  "lang_code": "en",
  "meronyms": [
    {
      "word": "base field"
    },
    {
      "word": "extension field"
    }
  ],
  "pos": "noun",
  "related": [
    {
      "word": "extension"
    },
    {
      "word": "extension field"
    }
  ],
  "senses": [
    {
      "categories": [
        "English countable nouns",
        "English entries with incorrect language header",
        "English lemmas",
        "English multiword terms",
        "English nouns",
        "English terms with quotations",
        "en:Algebra",
        "en:Algebraic geometry"
      ],
      "examples": [
        {
          "ref": "1974, Thomas W. Hungerford, Algebra, Springer, page 230",
          "text": "A Galois field extension may be defined in terms of its Galois group (Section 2) or in terms of the internal structure of the extension (Section 3).",
          "type": "quotation"
        },
        {
          "text": "1998, David Goss, Basic Structures of Function Field Arithmetic, Springer, Corrected 2nd Printing, page 283,\nNote that the extension of L obtained by adjoining all division points of ψ includes at most a finite constant field extension."
        },
        {
          "text": "2007, Pierre Antoine Grillet, Abstract Algebra, Springer, 2bd Edition, page 530,\nA field extension of a field K is, in particular, a K-algebra. Hence any two field extensions of K have a tensor product that is a K-algebra."
        }
      ],
      "glosses": [
        "Any pair of fields, denoted L/K, such that K is a subfield of L."
      ],
      "links": [
        [
          "algebra",
          "algebra"
        ],
        [
          "algebraic geometry",
          "algebraic geometry"
        ],
        [
          "fields",
          "field#English"
        ],
        [
          "subfield",
          "subfield"
        ]
      ],
      "qualifier": "field theory",
      "raw_glosses": [
        "(algebra, field theory, algebraic geometry) Any pair of fields, denoted L/K, such that K is a subfield of L."
      ],
      "topics": [
        "algebra",
        "algebraic-geometry",
        "geometry",
        "mathematics",
        "sciences"
      ],
      "wikipedia": [
        "field extension"
      ]
    }
  ],
  "translations": [
    {
      "code": "fi",
      "lang": "Finnish",
      "sense": "pair of fields such that one is a subfield of the other",
      "word": "kuntalaajennus"
    }
  ],
  "word": "field extension"
}