**Definition :** Let be a set and be a operation. must be associative and have an identity element under .

is a monoid if for all then and there exists an element such that for all then .

**See also :** Group, Ring, Binary Operation

**Definition :** Let be a set and be a operation. must be associative and have an identity element under .

is a monoid if for all then and there exists an element such that for all then .

**See also :** Group, Ring, Binary Operation