Migration And Topology Migration Semigroup

In this dissertation,we mainly consider transitive linear semigroups and topologically transitive linear semigroups of M_n(C).This dissertation consists of five sections.The first section is introduction and preliminaries.In the second section,we obtain the relation between the transitive linear semigroup and the transitive linear group when the transitive linear semigroup is right t-simple transitive linear semigroup.Also,we give two equivalent conditions for a right ideal of the transitive linear semigroup to be transitive.In the third section,we consider the t-simple transitive linear semigroups,we give some equivalent conditions for a two-sides ideal of the transitive linear semigroup to be transitive.Also,we give the explicit forms of the minimal t-simple transitive linear semigroups.The concept of semi-transitive linear semigroup is introduced in the fourth section. We give some equivalent conditions for a left ideal and a two-sides ideal of the semitransitive linear semigroup to be t-simple semi-transitive.We show that all nonzero elements in a st-simple semi-transitive linear semigroup have the same rank.In the last section,we consider the semigroups of linear transformations that act topologically transitively on a finite-dimensional vector space.We investigate the relation between the groups and the semigroups that lack the proper topologically transitive left ideals.Some explicit forms are given for the topologically transitive left ideal of topologically transitive semigroups.Finally we give some examples to show that neither the condition "nonzero nilpotent" is sufficient nor the condition" similar to a strict contraction" is sufficient in Example 11 in reference[7].