In this section we Define a simple mathematical system,consisting of a set together with a binary operation,that has many Important application.
A semigroup is a non empty set S together with an associative binary operation * defined On S.We shall denote the semi group by(S,*)or, when it is clear what the operation * is,simply by s.We also refer to a*b as the product of a and b.
The semigroup (S,*)is said to be commutative if * is a commutative operation.
Example 1. The set P(S) ,where S is a set,together with the operation of union is commutative semi group.
Example 2. Let(L<=)be a latices.Define a binary operation on L by a*b=a V b.Then L is a semigroup