中文摘要：

引进了简单迹极限的相关概念，简单介绍了与C^＊代数SP性质密切相关的F性质，并且得到了非基本的单的具有SP性质的C^＊代数具有F性质．在此基础上得出简单迹极限的基本可比性．其主要结果：设A为具有F性质的带单位元1的C^＊代数，且A的迹态空间T（A）为非空集，如果对每个自然数n，An具有基本可比性，则An的简单迹极限A也具有基本可比性。

英文摘要：

An introduction to the definition of the simple tracial limit of C^＊-algebra is first made in this paper. Then, the relationship between the property （SP） and the property F of C^＊-algebra A is studied. A perfect conclusion is obtained on fundamental comparison of simple tracial limit： Let A be a unital C^＊ -algebra with the property F the tracial space of A nonempty, if A, has the property of fundamental comparison for each natural number n, then, simple tracial limit of An has the property of fundamental comparison.