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  "body": "\n## Summary\n\nAn equational basis of a class of algebras is a set of [[identities|PKD440G2XW]] from which all identities of the class follow.\nIt is a set of axioms for the [[equational theory|F1M51B4MDG]] of the class, and it defines the [[variety|AJNZJD8442]] generated by the class.\nThe usual axioms of groups, rings or lattices are equational bases, and a central question is whether a given algebra has a finite one.\n\n## Explanations\n\n### L1 human\n\nAn algebra satisfies infinitely many laws, and an equational basis is a list of laws from which all the others can be derived.\nFor groups, written with multiplication, inverse and identity element, three short laws suffice: associativity, $x e \\approx x$ and $x x^{-1} \\approx e$.\nEvery other law that holds in all groups, such as $(x y)^{-1} \\approx y^{-1} x^{-1}$, can be derived from these.\nA basis is useful because it is much shorter than the full list of laws.\n",
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