In mathematics, a semigroup is an algebraic structure consisting of a set S closed under an associative binary operation. In other words, a semigroup is an associative magma. The terminology is derived from the anterior notion of a group.
The operation of a semigroup is most often denoted multiplicatively, that is, x·y or simply xy denotes the result of applying the semigroup operation to the ordered pair (x, y).
The formal study of semigroups began in the early 20th century. Since the 1950s, the theory of finite semigroups has been of particular importance in theoretical computer science because of the natural link between finite semigroups and finite automata
Reference:
http://en.wikipedia.org/wiki/Semigroups
