Of ¦Ð-positive Semigroup On Weak Natural Partial Order Relations And Applications

After establishing the defination of the weak natural order of π—regular semigroup, we investigate the related character of kinds of π—regular semigroup. This dissertation consists of 8 sections.The first two sections are introduction and preliminaries respectively.After introducing the basic definations related, we give the defination of the weak natural order of π—regular semigroup: Va, b ∈S,a≤b=a≤b=a = eb =bf,(e,f∈E(S)).In the third section,we investigate many character of π—regular semigroup with the defination of the weak natural order.We define the majorization , mi-norization , covering and investigate the related character.GV—semigroup is investigated in section 4.After defining the retract of semigroup and retract ideal, combining with majorization and minorization, we investigate the related character of the defination of the weak natural order we argued.Lemma 4 . 4(2) Seta ∈ S_α,α≥β,then:(?)b∈ Sβ,so thatα ≥ b.This lemma offer basic for the later theorem of the structure of normal π—cryptogroup in section 7.The fifth section gives the expression of the weak natural order on strong π—inverse semigroup and investigates many characters of that semigroup.The characters of π—cryptogroup and normal π—cryptogroup are investigated in section 6 and 7.In the 7th section,athe defination of similar class as follow: We name Sa as the similar class which a lies in, if Va, b ∈ Sa , s.t a = b , that is a ~ b.Theorem 7 . 7Normal π—cryptogroup is the class strong semilattice of completely achimedean semigroup.It gives the structure theorem of normal π—cryptogroup: A normal π—crypto...