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  "body": "\n## Summary\n\nA magma is a set with one [[binary operation|0M418FE7BB]] and no further axioms.\nIt is the most basic [[algebraic structure|QJGPT2W0FT]] with a binary operation: [[semigroups|0XMEM406JM]], [[monoids|0N6R902FG1]], [[groups|G5S1M9]] and quasigroups are magmas with extra conditions.\nOlder texts call a magma a groupoid, a name that now usually means something else in category theory.\n\n## Explanations\n\n### L1 human\n\nA magma is a set where any two elements can be combined into a third, in a fixed order.\nNo rule is asked for: the result may depend on how you place brackets and on the order of the two elements.\nSubtraction on the integers is an example: $5 - 3$ is an integer, but $(5 - 3) - 1 \\ne 5 - (3 - 1)$.\nMany familiar structures are magmas with additional rules, so facts about magmas hold for all of them.\n",
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