algebra Definition Unitality A relation ∘ over a set S is called unital if there exists an element e∈S such that: ∃e∈S:∀x∈S:e∘x=x∘e=x Such an element e is called a neutral element or identity element. Relation to Other Structures Monoid A monoid is precisely a semigroup (an associative relation) that is also unital.