Primitivity of Residually Finite Dimensional and Exponential in Simple Z-Stable 𝐂�∗-Algebras

Abstract

We show that Primitively of unital full free products of residually finitedimensional𝐶∗-algebra and clear that the homeomorphisms into Z-Stable 𝐶∗-algebra. We explained that the exponential rank and exponential length to 𝐶∗-algebra and Z-Stable as well as we explained equivalence approximate unitary of tracial Rank one . We studied homology of unitaries in simple 𝐶∗-algebra and through that we present to the result of equivalence approximate unitary with tracial rank one. Finally we give the uniqueness and the theory of existence and classfication theorms to obtain nuclear simple 𝐶∗-algebraresults of tracial topological rank one.