In Several Types Of Regular Semigroups Pastijn Plot Structure And Its Congruence Research

The objectives of this thesis are the congruences on locally inverse semigroups, locallyL-unipotent semigroups and the structures of locally orthodox semigroups.At the beginning the representatives of elementary rectangular band of E-unitary in-verse semigroups is studied, with the congruences on lattices and on completely simplesemigroups the congruences and congruence lattices on elementary rectangular band ofE-unitary inverse semigroups are described.In the second part based on the obtained descriptions of congruences and congruencelattices on elementary rectangular band of E-unitary inverse semigroups the Kernel-Trace operators and the structure the operator semigroups generated by the four oper-ators on the congruence lattices on elementary rectangular band of E-unitary inversesemigroups are described. The results obtained in this part are generalizations of re-sults of the operators semigroup on completely simple semigroups.In the third part the congruence lattices consisted of band congruences on the band ofL-unipotent semigroups are discussed. Some classes of band of L- unipotent semi-groups are described with the band congruences.Finally with the tool of Pastijn product a class of locally orthodox semigroups areconstructed by using bands and completely simple semigroups, and the classification ofthe forms of the Pastijn product on this class is discussed. Then the condition thatthe locally orthodox semigroups having the structure of Pastijn product are locallyinverse semigroups is given.