The Relationship Between The Two Types Of Ordered Semigroups Of Semilattice Decomposition And Several Types Of Ordered Semigroups

Algebraic theory of partially ordered semigroups is still one of the most active fields of algebra.The main goal of this dissertation is to give us the de-compositions of two types of ordered semigroups.Secondly, this dissertation gives us the relations between some types of ordered semigroups and some properties of partially ordered semigroups' homomorphism. It mainly achieved in the fol-lowing aspects:1. The decomposition of the intra-regular and duo ordered semigroups is given.An ordered semigroup is intra-regular and duo if and only if it is a semi-lattice of intra-regular and simple and left simple and right simple sub-semigroups.2. The characterizations of the left-regular and duo ordered semigroups are given out by a series of equivalence propositions.An left-regular and duo ordered semigroup is in accordance with a semi-lattice of left-regular and left simple and right simple sub-semigroups.3. We studied the relations between some types of ordered semi-groups,i.e. there are some relations between the different types of ordered semi-groups in which some of the terms including left-regular,right-regular,intra-regular,regular,left duo,right duo and duo are added.Then we studied some properties of the ordered semigroups' homomorphism.