"prime field" meaning in All languages combined

{
  "forms": [
    {
      "form": "prime fields",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "prime field (plural prime 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"
        }
      ],
      "examples": [
        {
          "text": "1968, J. F. Schuh, Mathematical Tools for Modern Physics, Philips Technical Library, page 91,\nTheorem 2. Each field contains a unique prime field."
        },
        {
          "text": "2004, H. Gopalkrishna Gadiyar, K. M. Sangeeta Maini, R. Padma, Cryptography, Connections, Cocycles and Crystals: A p-adic Exploration of the Discrete Logarithm Problem, Anne Canteaut, Kapaleeswaran Viswanathan (editors), Progress in Cryptology - INDOCRYPT 2004: 5th International Conference, Proceedings, Springer, LNCS 3348, page 305,\nApplying Hensel's lemma to the discrete logarithm problem over prime fields reveals the rich geometric and algebraic structure underlying the problem."
        },
        {
          "ref": "2004, Leo Corry, Modern Algebra and the Rise of Mathematical Structures, 2nd edition, Springer (Birkhäuser), page 194",
          "text": "Since every field contains a prime field, by studying prime fields, and the way properties are passed over to extensions, Steinitz would attain a full picture of the structure of all possible fields.",
          "type": "quotation"
        }
      ],
      "glosses": [
        "A field that contains no proper subfields."
      ],
      "id": "en-prime_field-en-noun-Btb1pJbX",
      "links": [
        [
          "algebra",
          "algebra"
        ],
        [
          "field",
          "field"
        ],
        [
          "proper",
          "proper"
        ],
        [
          "subfield",
          "subfield"
        ]
      ],
      "qualifier": "field theory",
      "raw_glosses": [
        "(algebra, field theory) A field that contains no proper subfields."
      ],
      "topics": [
        "algebra",
        "mathematics",
        "sciences"
      ]
    }
  ],
  "word": "prime field"
}

{
  "forms": [
    {
      "form": "prime fields",
      "tags": [
        "plural"
      ]
    }
  ],
  "head_templates": [
    {
      "args": {},
      "expansion": "prime field (plural prime fields)",
      "name": "en-noun"
    }
  ],
  "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",
        "English terms with quotations",
        "en:Algebra"
      ],
      "examples": [
        {
          "text": "1968, J. F. Schuh, Mathematical Tools for Modern Physics, Philips Technical Library, page 91,\nTheorem 2. Each field contains a unique prime field."
        },
        {
          "text": "2004, H. Gopalkrishna Gadiyar, K. M. Sangeeta Maini, R. Padma, Cryptography, Connections, Cocycles and Crystals: A p-adic Exploration of the Discrete Logarithm Problem, Anne Canteaut, Kapaleeswaran Viswanathan (editors), Progress in Cryptology - INDOCRYPT 2004: 5th International Conference, Proceedings, Springer, LNCS 3348, page 305,\nApplying Hensel's lemma to the discrete logarithm problem over prime fields reveals the rich geometric and algebraic structure underlying the problem."
        },
        {
          "ref": "2004, Leo Corry, Modern Algebra and the Rise of Mathematical Structures, 2nd edition, Springer (Birkhäuser), page 194",
          "text": "Since every field contains a prime field, by studying prime fields, and the way properties are passed over to extensions, Steinitz would attain a full picture of the structure of all possible fields.",
          "type": "quotation"
        }
      ],
      "glosses": [
        "A field that contains no proper subfields."
      ],
      "links": [
        [
          "algebra",
          "algebra"
        ],
        [
          "field",
          "field"
        ],
        [
          "proper",
          "proper"
        ],
        [
          "subfield",
          "subfield"
        ]
      ],
      "qualifier": "field theory",
      "raw_glosses": [
        "(algebra, field theory) A field that contains no proper subfields."
      ],
      "topics": [
        "algebra",
        "mathematics",
        "sciences"
      ]
    }
  ],
  "word": "prime field"
}