# Monoid

Definition : Let $G$ be a set and $*$ be a operation. $G$ must be associative and have an identity element under $*$.

$G$ is a monoid if for all $a, b, c \in G$ then $a * (b*c) = (a*b)*c$ and there exists an element $e$ such that for all $a \in G$ then $a * e = a$.