中文摘要：

本文引入了一类迹稳定秩一的C^＊-代数，证明了迹稳定秩一的C^＊-代数与AF-代数的张量积是迹稳定秩一的，得到了一个可分的单的有单位元的迹稳定秩一的，并且具有SP性质的C^＊-代数是稳定秩一的．同时，还讨论了迹稳定秩一的C^＊-代数的K-群的某些性质．

英文摘要：

In this paper, we will introduce a class of C^＊-algebras which have tracially stable rank one; we show that if A is a unital C^＊-algebra with tracially stable rank one and B is an AF-algebra, then A × B has tracially stable rank one; if A is a separable simple unital C^＊-algebra which has tracially stable rank one and SP property then it has stable rank one. We also get some properties about K-group of a separable unital C^＊-algebra with tracially stable rank one.