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  "body": "\n## Summary\n\nA unital magma is a [[magma|9689SFPVE9]] with an [[identity element|07WYQPB8E3]], an element that leaves every element unchanged when combined with it on either side.\nThe identity of a unital magma is unique.\nA [[monoid|0N6R902FG1]] is exactly an associative unital magma, and loops in the theory of quasigroups are unital magmas with unique solutions of equations.\n\n## Explanations\n\n### L1 human\n\nA unital magma has a neutral element $e$: combining $e$ with any $x$, in either order, gives back $x$.\nNo other rule is asked for.\nFor example, the integers with $x * y = x + y + xy$ have neutral element $0$, since $0 * y = y$ and $x * 0 = x$.\nIf two elements $e$ and $e'$ were both neutral, then $e = e * e' = e'$, so there is only one.\n",
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