Unital magma

A magma $(M,*)$ is said unital if there exists an element $e\in M$, called identity element, such that for all $x\in M$:
$$x*e=x=e*x.$$

Remarks

• The identity element is unique.

Examples

$\bullet$ If $(M,*)=(\Z,+)$, then $e=0$.
$\bullet$ If $(M,* )=(\R^*,\cdot)$ then $e=1$.