Study On The Structures Of Some Generalized Regular Semigroups

In this dissertation,we mainly give some structure theorems of generalized regular semigroups.There are six chapters,the main contest are given in follow:In the first chapter:we give the introductions and preliminaries.In the second chapter:we mainly discuss the structure of PI-strong L-abundant semigroups.The main result is given in follow:Theorem 2.2.4.S is a PI-strong L-abundant semigroup if and only if S is a spined product B×YT of a normal band B=[Y;Eα;ψα,β] and an exchanged C-L-abundant semigroup T=[Y;Tα;ψα,β] about semilattice Y.In the third chapter:we mainly discuss the structure of prefect L-abundant semigroups.The main result is given in follow:Theorem 3.2.5 S is a strong L-abundant semigroup,then S is a prefect L-abundant semigroups if and only if S is an orthordox loally C-L-abundant semigroup.Theorem 3.3.2 Let S is semigroup,then the following conditions are equivalent:(1)S is a perfect L-abundant semigroup；(2)L is a congruence,and S is a spined prouduct of the C-L-abundant semi-group and a normal band；(3)C is a congruence,and S is a strong lattice of unipotent planks.In the fourth chapter:we mainly discuss the structure ofρ-abundant semigroups with weak normal idempotents.The main result is given in follow:Theorem 4.3.3 In the semigroup(SQ,.),ρ' is a congruence definded as in the theorem 4.3.2,(x,s,y)(?)(u,t,v)∈SQ then the following conditions are true:(1)(x,s,y)∈E(SQ)if and only if spyzs=s;(2)(x,s,y)Rρ'(u,t,v)if and only if x=u,sRρt;(3)(x,s,y)(?)ρ'(u,t,v)if and only if s(?)ρt,y=v; (C5)If x∈Lsρ+,y∈Rsρ* and s=spyxs,means s=pyx∈Y,then the following twe conditions are true:(4)SQ isρ'-abundant semigroup；(5)(εl,ε,εr)is an idemotent of SQ.Theorem 4.3.4 Let(T,L,R,P))is SQ-system,if P satisfies(C5),then there exist a congruenceρ' such that SQ(T,L,R,P))is aρ'-abundant semigroup with a weak normal idempotent(εl,ε,εr),otherwise veryρ-abundant semigroup with weak normal idempotent can be constructed by this wayIn the fifth chapter:we mainly discuss the structure ofρ-abundant semigroups with normal medial idempotents.The main result is givon in follow:Lemma 5.2.2 There exist a congruenceρ(?) on W that make W is aρ'-abundant semigroup,and1)E(W)={(e,x,f)∈W|x∈E°,fe=x);2)E(W)={(e,x,f)∈W |x∈E°)≌E;3)(u,u,u)is a normal midial idempotent of W；4)(u,u,u)W(u,u,u)≌S.Theorem 5.2.5 let S is aρ-abundant semigroup with a normal medial idempotent u,E=is a regular semigroup of idempotent generated,then S≌W(E,uSu).