{
  "aliases": null,
  "backlinks": [
    {
      "field": "defines",
      "target": "DZ0B0JD11D"
    }
  ],
  "body": "\n## Summary\n\nA minimal variety is a nontrivial [[variety|AJNZJD8442]] of algebras whose only proper [[subvariety|4YSCK1DF26]] is the trivial variety.\nMinimal varieties are the atoms of the [[lattice of subvarieties|GJAYCVYZYF]] of a variety.\nEvery nontrivial variety contains at least one minimal variety.\n\n## Explanations\n\n### L1 human\n\nA minimal variety is as small as a variety can be without being trivial.\nIf one adds to its defining identities any identity that does not already hold in it, only one-element algebras are left.\nThe variety of Boolean algebras is an example.\nEach Boolean algebra with at least two elements contains the two-element Boolean algebra, and that algebra generates the whole variety.\n",
  "commit": "ff8a40749dc16545e3d2fc637f6b0196e81d0bfa",
  "front": {
    "kind": "concept",
    "msc": [
      "08B15"
    ],
    "name": "Minimal variety",
    "sources": [
      {
        "url": "https://en.wikipedia.org/wiki/Variety_(universal_algebra)"
      }
    ],
    "specializes": [
      "AJNZJD8442"
    ],
    "tag": "JXH66D0XD5"
  },
  "kind": "concept",
  "link": "https://tamnd.github.io/math2/node/JXH66D0XD5/",
  "links": [
    {
      "field": "specializes",
      "target": "AJNZJD8442"
    }
  ],
  "markdown": "https://tamnd.github.io/math2/node/JXH66D0XD5.md",
  "msc": [
    "08B15"
  ],
  "name": "Minimal variety",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/JXH/JXH66D0XD5.md",
  "status": null,
  "tag": "JXH66D0XD5",
  "uri": "m2://JXH66D0XD5",
  "url": "https://tamnd.github.io/math2/wiki/minimal-variety/",
  "writing": {
    "tag": "JXH66D0XD5",
    "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
      }
    ]
  }
}