Matricial Field（MF）代数是Blackadar和Kirchberg在1997年利用广义归纳极限定义的。本项目将首先深入探讨MF代数的结构，并进一步分析RFD代数，内拟对角代数和一般的拟对角代数之间的关系。在此基础上本项目将分析内拟对角代数的自由积和交叉积的结构。.本项目的第二部分将研究拓扑自由熵维数。2002年D. Voiculescu引入拓扑自由熵维数 (topological free entropy dimension) 的概念。拓扑自由熵维数良定义需要C*-代数为MF代数。本项目将研究拓扑轨道维数(topological orbit dimension)的性质和取值情况，并利用其与拓扑自由熵维数的关系进一步分析拓扑自由熵维数。最后本项目将计算一些与MF性质有关的C*-代数的相似度，这部分内容与Kadison 的 Similarity Problem相关.

Matricial Field（MF）algebras were first introduced by Blackadar and Kirchberg in 1997 by using generalized inductive limit. In this project, we are going to analyze the structure of MF algebras. We will discuss the relation between RFD algebras, inner quasidiagonal C*-algebras and general quasidiagonal C*-algebras. Based on these research, we will consider the free products of inner quasidiagonal C*-algebras and cross products of inner quasidiagonal C*-algebras . .The second part of this project is to consider the topological free entropy dimension In 2002, D. Voiculescu introduced topological free entropy dimension. It is well- known that topological free entropy dimension of an algebra is well defined if and only if the given algebra is MF. We are going to analyze the properties of topological orbit dimension and then give more information of topological free entropy dimension by using the relation between topological orbit dimension and topological free entropy dimension. At last, we are going to discuss the similarity degree of some C*-algebras which are connected to MF property. This part is related to Kadison's similarity problem.