Regular H-semigroup L ~ * Left Sub-semigroups,

The research of order semigroups plays an important part in the research of the theory of semigroups. Many experts and scholars thorough, painstakingly and investigate it. In this paper, we mainly study the properties of the (?)* left order semigroups and the (?)* straight left orders, and give some quite general conditions for a (?)* left order semigroup to be (?)* straight. Meanwhile, we characterize the (?)* left order semigroups in regular H-semigroups by so-called (?)*suitable pairs.In chapter 1, we simply introduce the background and the present state of the theory of order semigroups;for the sake of convenience, we introduce some fundamental knowledge about order semigroups. In chapter 2, firstly, we study some properties of the (?)* left order semigroups and the (?)* straight left orders. Secondly, we study the relations of several local semigroups. Thirdly, we give a binary relation on (?)*LO_q. In chapter 3, we mainly characterize the (?)* left order semigroups in regular H-semigroups by so-called (?)*suitable pairs, then give several equivalent descriptions for it. In chapter 4, we characterize the (?)* stratified left order semigroups in regular H-semigroups, and give some results of the (?)* left order semigroups to the left order semigroups.