monoid

幺半群 monoid

A monoid is a triple $(X,\square ,i)$ consisting of a set X, a binary operation □, and a special element $i\in X$ (called the identity element of X), satisfying these rules:

(associative law)

$(x\square y)\square z=x\square (y\square z)$

(identity law)

$x\square i=x=i\square x$

for all $x,y,z\in X$.

A monoid is a semigroup with an identity element.