Several Studies Semigroups Order Г-

In this paper, we introduce the concept ideals of po-Г-semigroups. The generation theorem of ideals is obtained by every non-emptyset of po-Г-semigroups. Characterlizations of simple po-Г-semigroups, and regular po-Г-semigroups are given by ideals. Finally, we prove the em-bedding theorem of hypersemigroups in terms of fuzzy sets. To sum up, the main content of this thesis as follows:In chapter2, we introduce the notion of ideals of of po-Г-semigroups. Then we show that many results on (m, n) ideals of semigroups can be extended to (m, n) ideals of po-Г-semigroups, in which we show results including some characterizations of the nonempty join of all (m, n) ideals of a po-Г-semigroup is a (m,n) ideal. Meanwhile, the generation theorem of (m,n) ide-als and the characterizations of simple po-Г-semigroups by minimal (m,n) ideals are intro-duced.Finally, we give some characterizations of regular po-Г-semigroups are given by (m, n) ideals.In chapter3, we introduce the notion of quasi-ideals in po-Г-semigroups. Then we show that many results on quasi-ideals of po-Г-semigroups can be extended to (m, n)-quasi-ideals of po-Г-semigroups, in which we show results including the nonempty join of all (m,n)-quasi-ideals of a po-Г-semigroup is an (m, n)-quasi-ideal,and the intersection of an m-left-ideal and an n-right-ideal is an (m, n)-quasi-ideal is introduced.Meanwhile, we show that generation theo-rems and minimal properties among (m, n)-quasi-ideals, m-left-ideals and an n-right-ideals.Finally, we give some the characterizations of simple po-Г-semigroups by (m, n)-quasi-ideals.In chapter4, the set of fuzzy points, inclusion homomorphism and strong homomorphism in hypersemigroups is introduced. We proved that the set of all fuzzy subsets of a hypersemi-group by the multiplication and the order relation we had given which is a semigroup and a partially ordered semigroup with the greatest element. Then, we show that hypersemigroups can be effectively embedded in it.