<![CDATA[In this paper, its discussed about the construction of regular semigroup, orthodox semigroup, including inverse semigroup and band. A natural order in S for the regular semigrup is given by with . Semigroup S is called pure if for and , then . The purpose of this research is to determine the condition of the natural order on some regular semigrup construction and its relationship with E-unitary and pure semigrup. Pure semigroup and and E-unitary is a special condition of the natural order. There is a natural order that is not a partial order. Natural order can be defined in some semigroup construction. In a mapping, there is a purity that influence each other, and also by inverse semigrup.]]>
