Some Researches On Completely 0-Simple Semigroups

In this thesis, by using of the Rees matrix-representation of completely 0-simple semigroups and"linked triple"characterization of proper congruenceson them, we investigate the following three basic questions :1. Characterization of the structure of proper homomorphic images of a com-pletely 0-simple semigroup ;2. Characterization of the maximum proper congruence, idempotent-purecongruences, idempotent-separating congruences and 0-group congruences of acompletely 0-simple semigroup and the corresponding congruence-lattices or ho-momorphic images ;3. Characterization of the structure of completely 0-simple weakly inversesemigroups.The thesis is divided into three chapters.In the first chapter, we first give a new characterization of proper congruenceson a completely 0-simple semigroup with normal Rees matrix representation S =M0[G;I,Λ;P]. This characterization is quite close to the characterization ofcongruences on a group by the cosets of a normal subgroup. Then we provethat any proper homomorphic image of a completely 0-simple semigroup is alsocompletely 0-simple and we give their Rees matrix constructions.In the second chapter, by using of the isomorphism between the congruence-lattice and the lattice of all linked triples on a completely 0-simple semigroup, we...