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+ | ====== Monoid ====== | ||
+ | |||
+ | Monoid is a triple $(G, *,e)$ where ${*} : G^2 \to G$ such that | ||
+ | * $(G,*)$ is a [[semigroup]] and | ||
+ | * $e$ is a neutral element for $*$ | ||
+ | The second condition means that for all $x \in G$, | ||
+ | \begin{equation*} | ||
+ | x * e = e * x = x | ||
+ | \end{equation*} | ||