{
  "aliases": null,
  "backlinks": [
    {
      "field": "instance_of",
      "target": "2BVB7YDEV4"
    },
    {
      "field": "instance_of",
      "target": "ZZF8XPBG3Z"
    },
    {
      "field": "uses",
      "target": "2BVB7YDEV4"
    },
    {
      "field": "uses",
      "target": "ZZF8XPBG3Z"
    },
    {
      "field": "defines",
      "target": "3H2W1MQFGM"
    }
  ],
  "body": "\n## Summary\n\nAn absolutely free algebra is an algebra that is free in the class of all algebras of its signature, with no identities imposed at all.\nUp to isomorphism, the absolutely free algebra on a set $X$ is the [[term algebra|3YYKGWJJND]] over $X$, whose elements are the formal terms.\nEvery free algebra of a variety is a quotient of an absolutely free algebra, so terms are the common raw material of all free algebras.\n\n## Explanations\n\n### L1 human\n\nTake generators $x, y$ and one binary operation $*$.\nBuild every expression, such as $x * y$, $(x * y) * x$ and $x * (y * x)$, and treat two expressions as equal only when they are written the same way.\nThis algebra satisfies no law, not even $x * y = y * x$ or associativity.\nIt is \"absolutely\" free because no rule restricts it.\n",
  "commit": "ff8a40749dc16545e3d2fc637f6b0196e81d0bfa",
  "front": {
    "kind": "concept",
    "msc": [
      "08B20",
      "08A40"
    ],
    "name": "Absolutely free algebra",
    "sources": [
      {
        "url": "https://en.wikipedia.org/wiki/Term_algebra"
      }
    ],
    "specializes": [
      "GTS4DRRMZR"
    ],
    "tag": "TTTEV3NWWM"
  },
  "kind": "concept",
  "link": "https://tamnd.github.io/math2/node/TTTEV3NWWM/",
  "links": [
    {
      "field": "specializes",
      "target": "GTS4DRRMZR"
    }
  ],
  "markdown": "https://tamnd.github.io/math2/node/TTTEV3NWWM.md",
  "msc": [
    "08B20",
    "08A40"
  ],
  "name": "Absolutely free algebra",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/TTT/TTTEV3NWWM.md",
  "status": null,
  "tag": "TTTEV3NWWM",
  "uri": "m2://TTTEV3NWWM",
  "url": "https://tamnd.github.io/math2/wiki/absolutely-free-algebra/",
  "writing": {
    "tag": "TTTEV3NWWM",
    "kind": "concept",
    "level": "W0",
    "next": [
      {
        "what": "an inventory row",
        "note": "the row of the inventory that the node accounts for",
        "have": 0,
        "want": 1
      },
      {
        "what": "a source with a locator",
        "have": 0,
        "want": 1
      }
    ]
  }
}