Monoid

Definition: Monoid

A monoid $(M,\circ )$ is a set $M$ equipped with a binary operation $\circ :M\times M\to M$ which has the following properties.

• Associativity: $(a\circ b)\cdot c=a\circ (b\circ c)$
• Existence of an identity element: $\exists e\in M:a\circ e=e\circ a=a$