Tracially Rank Of C～*-algebras And Quasidiagonal Extensions

In this paper, we introduce C~*-algebras of tracially tracial rank . give equivalent forms of definitions, and discuss some basic properties of this kind of C~*-algebras, such as property of hereditary matrix inductive limits direct sum and tensor products. Otherwise , based on [8] ,we discuss the quasidiagonal extension property of C~*-algebras of tracially tracial rank tracially real rank zero .