Unitality

algebra

Definition

Unitality

A relation $\circ$ over a set $S$ is called unital if there exists an element $e\in S$ such that:

$$\exists e\in S:\forall x\in S:e\circ x=x\circ e=x$$

Such an element $e$ is called a neutral element or identity element.

Relation to Monoids

A monoid is precisely a semigroup (an associative relation) that is also unital.