Noun
semigroup (plural semigroups)
(mathematics) Any set for which there is a binary operation that is closed and associative.
A 2-ary semigroup is just a semigroup. Source: Internet
A semigroup endowed with such an operation is called a U-semigroup. Source: Internet
A transformation semigroup can be made into an operator monoid by adjoining the identity transformation. Source: Internet
Conversely, the kernel of any semigroup homomorphism is a semigroup congruence. Source: Internet
Alternatively, a regular semigroup is inverse if and only if any two idempotents commute. Source: Internet
A semigroup without an identity element can be easily turned into a monoid by just adding an identity element. Source: Internet