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  "body": "\n## Summary\n\nAn algebra is finitely based when all of its [[identities|PKD440G2XW]] follow from finitely many of them, that is, when it has a finite [[equational basis|9Q008GMZSW]].\nEvery finite group, every finite ring and every finite lattice is finitely based, but some finite algebras are not.\nDeciding which finite algebras are finitely based is the subject of Tarski's finite basis problem.\n\n## Explanations\n\n### L1 human\n\nAny algebra satisfies infinitely many laws.\nIt is finitely based if a finite list of these laws is enough to derive all the others.\nThe integers under addition are finitely based: the laws of abelian groups give every law they satisfy.\nSurprisingly, there are algebras with only a few elements whose laws cannot be captured by any finite list.\n",
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