Some Studies On Some Generalized Regular Semigroups

In this paper, we are concerned with some generalized regular semigroups on thebasis of some general Green′s relations. Firstly, we introduce Green* relations andgive some properties of abundant 0-J*-simple ( J*-simple ) semigroup. Secondly,we presentρ-Green relations and o?er the constructing map of semisuperabundantsemigroup, then the homomorphisms and isomorphisms of semisuperabundant semi-group and the spined product are characterized. Finally, we bring in Green* rela-tions and reserch the translational hull of a strongly E-quasi-abundant semigroup,it is proved that the translational hull of a strongly E-quasi-abundant semigroup isa strongly E-quasi-abundant semigroup, the construction of the translational hull ofa strongly E-quasi-abundant semigroup is investigated further and it is proved thatthe semilattice of the translational hull is isomorphic to the the translational hull ofa semilattice.