{
  "aliases": null,
  "backlinks": [
    {
      "field": "specializes",
      "target": "0P3VCBDEE2"
    },
    {
      "field": "specializes",
      "target": "0PF6TM8TWT"
    },
    {
      "field": "specializes",
      "target": "0ZXZ82FTX2"
    },
    {
      "field": "specializes",
      "target": "634XKY8RZ0"
    },
    {
      "field": "specializes",
      "target": "8B57B7EGK4"
    },
    {
      "field": "specializes",
      "target": "D7YQW9RG24"
    },
    {
      "field": "specializes",
      "target": "GA5PTQGC6G"
    },
    {
      "field": "specializes",
      "target": "J85FZEQG38"
    },
    {
      "field": "specializes",
      "target": "MWBDFS2KJ5"
    },
    {
      "field": "specializes",
      "target": "NJ3APQ8BHH"
    },
    {
      "field": "defines",
      "target": "0QA8CHH8MG"
    },
    {
      "field": "uses",
      "target": "155K06F4JF"
    },
    {
      "field": "uses",
      "target": "1JCQTY728A"
    },
    {
      "field": "uses",
      "target": "1XYZNC2E6G"
    },
    {
      "field": "uses",
      "target": "2JDRN4ZS49"
    },
    {
      "field": "uses",
      "target": "312GG23DN4"
    },
    {
      "field": "uses",
      "target": "3S42WRMG9V"
    },
    {
      "field": "uses",
      "target": "56107GMFYV"
    },
    {
      "field": "uses",
      "target": "5FR6JX04RS"
    },
    {
      "field": "uses",
      "target": "5GCANV7337"
    },
    {
      "field": "uses",
      "target": "5WGZPE6249"
    },
    {
      "field": "uses",
      "target": "5ZKP6E4JCE"
    },
    {
      "field": "uses",
      "target": "6RXEC9CT6M"
    },
    {
      "field": "uses",
      "target": "778ZG6P6E6"
    },
    {
      "field": "uses",
      "target": "7TCB6AGE72"
    },
    {
      "field": "uses",
      "target": "7VJGH5BKKA"
    },
    {
      "field": "uses",
      "target": "7Z28JY8QW4"
    },
    {
      "field": "uses",
      "target": "8EV392NDQD"
    },
    {
      "field": "uses",
      "target": "8FEGZWG3JH"
    },
    {
      "field": "uses",
      "target": "8QTP2EFA92"
    },
    {
      "field": "uses",
      "target": "8ST7CTZ2DE"
    },
    {
      "field": "uses",
      "target": "94AKWRHND0"
    },
    {
      "field": "uses",
      "target": "99T7Z4T39W"
    },
    {
      "field": "uses",
      "target": "9MXPNHHMT1"
    },
    {
      "field": "uses",
      "target": "9ZBM46J88T"
    },
    {
      "field": "uses",
      "target": "9ZW7BCJMDT"
    },
    {
      "field": "uses",
      "target": "A7MZ6GG7W0"
    },
    {
      "field": "uses",
      "target": "AH7EW2EHNC"
    },
    {
      "field": "uses",
      "target": "AHCXQCYW3C"
    },
    {
      "field": "uses",
      "target": "AM07TESJED"
    },
    {
      "field": "uses",
      "target": "ARGNTXTAST"
    },
    {
      "field": "uses",
      "target": "B1Q5F5VNSK"
    },
    {
      "field": "uses",
      "target": "B6C3J2GJWP"
    },
    {
      "field": "uses",
      "target": "BGXEC1SVQV"
    },
    {
      "field": "uses",
      "target": "BPKZV9W7AT"
    },
    {
      "field": "uses",
      "target": "BT4QFQ9MJH"
    },
    {
      "field": "uses",
      "target": "BVR56STQ32"
    },
    {
      "field": "uses",
      "target": "CHT5JYM6QW"
    },
    {
      "field": "uses",
      "target": "DDY3Q3PJ6W"
    },
    {
      "field": "uses",
      "target": "DEV24TSWQZ"
    },
    {
      "field": "uses",
      "target": "ESRDNKF6WJ"
    },
    {
      "field": "uses",
      "target": "F7D849A4RZ"
    },
    {
      "field": "uses",
      "target": "FT3ERF0YP9"
    },
    {
      "field": "uses",
      "target": "GKV4RVXBRE"
    },
    {
      "field": "uses",
      "target": "GNEGMN4E26"
    },
    {
      "field": "uses",
      "target": "H30E38799N"
    },
    {
      "field": "uses",
      "target": "H8RN439272"
    },
    {
      "field": "uses",
      "target": "HFEA4FKGW1"
    },
    {
      "field": "uses",
      "target": "HP56DJECMT"
    },
    {
      "field": "uses",
      "target": "HQ0JN9W2PR"
    },
    {
      "field": "uses",
      "target": "J7GYAF4FGT"
    },
    {
      "field": "uses",
      "target": "JJZ5X28NNR"
    },
    {
      "field": "uses",
      "target": "KCVCPGX7ZC"
    },
    {
      "field": "uses",
      "target": "KPJED63FT6"
    },
    {
      "field": "uses",
      "target": "KVZ7D84541"
    },
    {
      "field": "uses",
      "target": "M5N08HD75V"
    },
    {
      "field": "uses",
      "target": "MV3PHCJ6CE"
    },
    {
      "field": "uses",
      "target": "N8YJAFVQRW"
    },
    {
      "field": "uses",
      "target": "NW7W4R0T85"
    },
    {
      "field": "uses",
      "target": "P0SYXV6RTK"
    },
    {
      "field": "uses",
      "target": "P32FQE1H0D"
    },
    {
      "field": "uses",
      "target": "PQB48WPK5C"
    },
    {
      "field": "uses",
      "target": "QBXW04EC4V"
    },
    {
      "field": "uses",
      "target": "QW17YJ6ZCT"
    },
    {
      "field": "uses",
      "target": "QYXGVES1XM"
    },
    {
      "field": "uses",
      "target": "R0DSZPRG6T"
    },
    {
      "field": "uses",
      "target": "RC5A5T7YY2"
    },
    {
      "field": "uses",
      "target": "RDV3C0PXTH"
    },
    {
      "field": "uses",
      "target": "RH6P1FGZSR"
    },
    {
      "field": "uses",
      "target": "RVEFNEJSHF"
    },
    {
      "field": "uses",
      "target": "SJ2BVG9F4W"
    },
    {
      "field": "uses",
      "target": "SMEFDN2RF5"
    },
    {
      "field": "uses",
      "target": "SXS38FWHEN"
    },
    {
      "field": "uses",
      "target": "SY22C7XVCW"
    },
    {
      "field": "uses",
      "target": "T942SHWSSF"
    },
    {
      "field": "uses",
      "target": "TAPCWE72R0"
    },
    {
      "field": "uses",
      "target": "TB3Q55Q0G4"
    },
    {
      "field": "uses",
      "target": "TPRFJNZ7S2"
    },
    {
      "field": "uses",
      "target": "TSX2MAA95V"
    },
    {
      "field": "uses",
      "target": "W3B4XH5JHZ"
    },
    {
      "field": "uses",
      "target": "W3YYX63R9R"
    },
    {
      "field": "uses",
      "target": "WXGM3VWEK6"
    },
    {
      "field": "uses",
      "target": "Y0SCJSFQ3B"
    },
    {
      "field": "uses",
      "target": "YBJ2VQHFDQ"
    },
    {
      "field": "uses",
      "target": "YC90FXM4SA"
    },
    {
      "field": "uses",
      "target": "YREPR562ES"
    },
    {
      "field": "uses",
      "target": "YX0J6TVGZ8"
    },
    {
      "field": "uses",
      "target": "YY8CG0NZ9C"
    },
    {
      "field": "uses",
      "target": "Z7MTTS6FFG"
    },
    {
      "field": "uses",
      "target": "ZCVB4ZQ0SA"
    },
    {
      "field": "uses",
      "target": "ZR6XXP36X8"
    },
    {
      "field": "uses",
      "target": "ZWPWF6NJC3"
    }
  ],
  "body": "\n## Summary\n\nA field is a commutative ring in which you can divide by every nonzero element.\nThe rational numbers, the real numbers and the complex numbers are fields.\nThe [[definition of a field|0QA8CHH8MG]] gives the axioms.\n",
  "commit": "ff8a40749dc16545e3d2fc637f6b0196e81d0bfa",
  "front": {
    "kind": "concept",
    "msc": [
      "12E99"
    ],
    "name": "Field",
    "same_as": {
      "wikidata": "Q190109",
      "wikipedia": "Field (mathematics)"
    },
    "sources": [
      {
        "locator": "lead section",
        "url": "https://en.wikipedia.org/wiki/Field_(mathematics)"
      }
    ],
    "specializes": [
      "0EA5BTA0CX"
    ],
    "tag": "04C5ZBG1WT"
  },
  "kind": "concept",
  "link": "https://tamnd.github.io/math2/node/04C5ZBG1WT/",
  "links": [
    {
      "field": "specializes",
      "target": "0EA5BTA0CX"
    }
  ],
  "markdown": "https://tamnd.github.io/math2/node/04C5ZBG1WT.md",
  "msc": [
    "12E99"
  ],
  "name": "Field",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/04C/04C5ZBG1WT.md",
  "status": null,
  "tag": "04C5ZBG1WT",
  "uri": "m2://04C5ZBG1WT",
  "url": "https://tamnd.github.io/math2/wiki/field/",
  "writing": {
    "tag": "04C5ZBG1WT",
    "kind": "concept",
    "level": "W1",
    "next": [
      {
        "what": "edge instance_of in",
        "note": "at least two examples",
        "have": 0,
        "want": 2
      },
      {
        "what": "edge not_instance_of in",
        "note": "at least one non-example",
        "have": 0,
        "want": 1
      }
    ]
  }
}