{
  "aliases": null,
  "backlinks": [
    {
      "field": "defines",
      "target": "052SDEPZH7"
    }
  ],
  "body": "\n## Summary\n\nAn irreducible element of an integral domain is a nonzero nonunit that is not a product of two nonunits.\nThe [[definition of an irreducible element|052SDEPZH7]] gives the conditions.\n",
  "commit": "545acf83a9b75c8ddc375ef8b23d2ae101a4d7e4",
  "front": {
    "kind": "concept",
    "msc": [
      "13A05"
    ],
    "name": "Irreducible element",
    "same_as": {
      "wikidata": "Q2989575",
      "wikipedia": "Irreducible element"
    },
    "sources": [
      {
        "locator": "lead section",
        "url": "https://en.wikipedia.org/wiki/Irreducible_element"
      }
    ],
    "tag": "0YMT0D2442"
  },
  "kind": "concept",
  "link": "https://math2.tamnd.com/node/0YMT0D2442/",
  "links": null,
  "markdown": "https://math2.tamnd.com/node/0YMT0D2442.md",
  "msc": [
    "13A05"
  ],
  "name": "Irreducible element",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/0YM/0YMT0D2442.md",
  "status": null,
  "tag": "0YMT0D2442",
  "uri": "m2://0YMT0D2442",
  "url": "https://math2.tamnd.com/wiki/irreducible-element/",
  "writing": {
    "tag": "0YMT0D2442",
    "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
      },
      {
        "what": "edge specializes both",
        "note": "the more general notions and the special cases",
        "have": 0,
        "want": 1
      }
    ]
  }
}
