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  "body": "\n## Summary\n\nA Mal'cev term of a [[variety|AJNZJD8442]] is a ternary term $p$ such that $p(x, y, y) = x$ and $p(x, x, y) = y$ hold in the variety.\nBy Mal'cev's theorem, a variety has a Mal'cev term exactly when it is a [[congruence-permutable variety|1B3N9T68YV]].\nGroups, rings, modules and quasigroups all have Mal'cev terms.\n\n## Explanations\n\n### L1 human\n\nIn a group, the formula $x y^{-1} z$ cancels the middle input against either neighbour.\nIf the last two inputs are equal, it returns the first, and if the first two are equal, it returns the last.\nA Mal'cev term is any formula with this cancelling behaviour.\nIts existence makes congruences, the ways of identifying elements, combine in either order with the same result.\n",
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