Monoid

A monoid is triple \(\left (\mathbb{M}, \cdot, 1 \right)\) such that:

• \(\mathbb{M}\) is an non-empty set
• \(\cdot : \mathbb{M} \times \mathbb{M} \rightarrow \mathbb{M}\) is an associative mapping, i.e., \(\forall t_1, t_2, t_3 \in \mathbb{M}, (t_1 \cdot t_2) \cdot t_3 = t_1 \cdot (t_2 \cdot t_3)\).
• \(1 \in \mathbb{M}\) is the unit satisfying \(1 \cdot t = t = t \cdot 1, \forall t \in \mathbb{M}\).