The Translational Hull Of Superabundant Semigroup

The theory of translational hull of semigroups is an important branch of the algebra theory and plays a basic role in the theory of ideal extensions of semigroups.The study of some kinds of semigroups mainly focus on searching for semigroups whose translational hull have the same structure as themselves. The main result include that: the translational hull of inverse semigroups are also inverse semigroups,that the translational hull of adequate semigroups are also adequate semigroups,and that the translational hull of type-A semigroups are also type-A semigroups . Meanwhile,the constructing of the translational hull of some kinds of semigroup was carried on,including the translational hull of completely 0-simple semigroup,and the structure of the translational hull of the Rees matrix in inverse monoid and so on .This paper mainly focuses on the study of the translational hull of superabundant semigroup.First,the structures of left(right) translational sets are built,then the translational hull of cancelative monoid are constructed . Moreover,the basic properties of these semigroup are described. Considering that the superabundant semigroups are semilattics of Rees matrix semigroup in cancelative monoid,stating from the homomorphism image and the translational hull of inner translations ,the paper probes into the structures of the translational hull of superabundant semigroups . Finally ,taking superabundant semigroup in which idempotents are central as an example ,which is a special kind of superabundant semigroups,the paper proves that the translational hull of such semigroups have the samestructure as themselves by constructing their idempotents.