{
  "aliases": null,
  "backlinks": [
    {
      "field": "defines",
      "target": "0GJ2HRG95T"
    },
    {
      "field": "instance_of",
      "target": "0K5W69AC0J"
    }
  ],
  "body": "\n## Summary\n\nA Euclidean domain is an integral domain with a division with remainder, in which the remainder is smaller than the divisor for some size function.\nThe integers and the polynomials over a field are the main examples.\nThe [[definition of a Euclidean domain|0GJ2HRG95T]] gives the conditions.\n",
  "commit": "6ac761d40018146541484a9e8b9eafd6ecc303dc",
  "front": {
    "kind": "concept",
    "msc": [
      "13F07"
    ],
    "name": "Euclidean domain",
    "same_as": {
      "wikidata": "Q867345",
      "wikipedia": "Euclidean domain"
    },
    "sources": [
      {
        "locator": "lead section",
        "url": "https://en.wikipedia.org/wiki/Euclidean_domain"
      }
    ],
    "tag": "0CHS7RBD39"
  },
  "kind": "concept",
  "link": "https://math2.tamnd.com/node/0CHS7RBD39/",
  "links": null,
  "markdown": "https://math2.tamnd.com/node/0CHS7RBD39.md",
  "msc": [
    "13F07"
  ],
  "name": "Euclidean domain",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/0CH/0CHS7RBD39.md",
  "status": null,
  "tag": "0CHS7RBD39",
  "uri": "m2://0CHS7RBD39",
  "url": "https://math2.tamnd.com/wiki/euclidean-domain/",
  "writing": {
    "tag": "0CHS7RBD39",
    "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
      }
    ]
  }
}