Semigroup

Definition

QUICK PHRASES: set with associative binary operation, group without identity element and inverses

Symbol-free definition

A semigroup is a set equipped with an associative binary operation.

A semigroup need not have an identity element.

The definition of semigroup does not require it to be nonempty, so the empty set is a semigroup. However, some variants of the definition require a semigroup to be a nonempty set with an associative binary operation.