{
  "aliases": null,
  "backlinks": [
    {
      "field": "defines",
      "target": "YNM6V0R269"
    }
  ],
  "body": "\n## Summary\n\nGumm terms are a finite chain of ternary terms of a [[variety|AJNZJD8442]].\nThey combine a chain like [[Jónsson terms|3M8Y76E4AG]] with a final step like a [[Mal'cev term|Y203PPTS61]].\nA variety has Gumm terms if and only if it is a [[congruence-modular variety|QAQAS3JWXW]].\nThis form of the Mal'cev condition for modularity shows that congruence modularity mixes the two basic cases, congruence distributivity and congruence permutability.\n\n## Explanations\n\n### L1 human\n\nLattices have a chain of formulas of one kind, and groups have one formula of another kind.\nGumm terms allow a chain of the lattice kind followed by one formula of the group kind.\nA variety has such a chain exactly when all its congruence lattices satisfy the modular law.\nSo congruence modularity sits between the lattice-like and the group-like behaviour, and contains both.\n",
  "commit": "ff8a40749dc16545e3d2fc637f6b0196e81d0bfa",
  "front": {
    "kind": "concept",
    "msc": [
      "08B05",
      "08B10"
    ],
    "name": "Gumm terms",
    "sources": [
      {
        "url": "https://en.wikipedia.org/wiki/Modular_lattice"
      }
    ],
    "tag": "SHMTFRH28E"
  },
  "kind": "concept",
  "link": "https://tamnd.github.io/math2/node/SHMTFRH28E/",
  "links": null,
  "markdown": "https://tamnd.github.io/math2/node/SHMTFRH28E.md",
  "msc": [
    "08B05",
    "08B10"
  ],
  "name": "Gumm terms",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/SHM/SHMTFRH28E.md",
  "status": null,
  "tag": "SHMTFRH28E",
  "uri": "m2://SHMTFRH28E",
  "url": "https://tamnd.github.io/math2/wiki/gumm-terms/",
  "writing": {
    "tag": "SHMTFRH28E",
    "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
      }
    ]
  }
}