Definition 1. Let $M$ be a magma and $e \in M$.
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$e$ is left-neutral if for all $a\in M$,
\[ea = a.\] -
$e$ is right-neutral if for all $a\in M$,
\[ae = a.\] -
$e$ is neutral if it is both left-neutral and right-neutral.
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$M$ is (left-/right-)unital if it has a (left-/right-)neutral element.