{
  "aliases": [
    "fraction-field",
    "quotient-field"
  ],
  "backlinks": [
    {
      "field": "instance_of",
      "target": "05K3J8J8T2"
    },
    {
      "field": "defines",
      "target": "0VF11ZTTMD"
    }
  ],
  "body": "\n## Summary\n\nThe field of fractions of an integral domain is the smallest field that contains it.\nIts elements are the fractions $a/b$ with $b \\neq 0$.\nThe rational numbers are the field of fractions of the integers.\nThe [[definition of the field of fractions|0VF11ZTTMD]] gives the construction.\n",
  "commit": "f591989ed15704e9d8755a7a5a6426d73de7a3ae",
  "front": {
    "aliases": [
      "fraction-field",
      "quotient-field"
    ],
    "kind": "concept",
    "msc": [
      "13B30"
    ],
    "name": "Field of fractions",
    "same_as": {
      "wikidata": "Q774579",
      "wikipedia": "Field of fractions"
    },
    "sources": [
      {
        "locator": "lead section",
        "url": "https://en.wikipedia.org/wiki/Field_of_fractions"
      }
    ],
    "tag": "0F2PTGX1A2"
  },
  "kind": "concept",
  "link": "https://math2.tamnd.com/node/0F2PTGX1A2/",
  "links": null,
  "markdown": "https://math2.tamnd.com/node/0F2PTGX1A2.md",
  "msc": [
    "13B30"
  ],
  "name": "Field of fractions",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/0F2/0F2PTGX1A2.md",
  "status": null,
  "tag": "0F2PTGX1A2",
  "uri": "m2://0F2PTGX1A2",
  "url": "https://math2.tamnd.com/wiki/field-of-fractions/",
  "writing": {
    "tag": "0F2PTGX1A2",
    "kind": "concept",
    "level": "W1",
    "next": [
      {
        "what": "edge instance_of in",
        "note": "at least two examples",
        "have": 1,
        "want": 2
      },
      {
        "what": "edge not_instance_of in",
        "note": "at least one non-example",
        "have": 0,
        "want": 1
      },
      {
        "what": "edge specializes both",
        "note": "the more general notions and the special cases",
        "have": 0,
        "want": 1
      }
    ]
  }
}