C ~ (*) - Trace The Extreme Nature Of The Closed Algebra,

The concept of rank is very important for the study of C*-algebras. A lot of ranks, for example: stable rank, real rank, tracial topological rank, analytic rank and so on, was introduced. These ranks have accelerated the development of C*-algebras.The introduction of tracial limit simplifies a lot of proofs concerned about the tracial topological rank.In this thesis,we try to show that there are some C'*-algebras maintaining the closing property with the tracial limit-especially under the condition of simple.