"prime field" meaning in English

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  "lang_code": "en",
  "pos": "noun",
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      "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": "quote"
        }
      ],
      "glosses": [
        "A field that contains no proper subfields."
      ],
      "id": "en-prime_field-en-noun-Btb1pJbX",
      "links": [
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          "algebra",
          "algebra"
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        [
          "field",
          "field"
        ],
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          "proper",
          "proper"
        ],
        [
          "subfield",
          "subfield"
        ]
      ],
      "qualifier": "field theory",
      "raw_glosses": [
        "(algebra, field theory) A field that contains no proper subfields."
      ],
      "topics": [
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        "mathematics",
        "sciences"
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  "word": "prime field"
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          "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."
        },
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          "ref": "2004, Leo Corry, Modern Algebra and the Rise of Mathematical Structures, 2nd edition, Springer (Birkhäuser), page 194:",
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      "glosses": [
        "A field that contains no proper subfields."
      ],
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      "qualifier": "field theory",
      "raw_glosses": [
        "(algebra, field theory) A field that contains no proper subfields."
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  "word": "prime field"
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