无限实秩C*-代数
C*-algebras of infinite real rank
摘要：
引入了单位$C^{\ast}$ -代数的弱（强）无限实秩的概念。证明了紧空间$X$是弱（强）无穷维的当且仅当$C(X)$具有弱（强）无穷实秩.还研究了这一概念的其他一些性质。特别地，证明了生成元可数的自由群的群$C^{\ast}$ -代数$C^{\ast}({\mathbb F}_{\infty})$具有强无穷实秩.
英文摘要：
We introduce the notion of weakly (strongly) infinite real rank for unital $C^{\ast}$-algebras. It is shown that a compact space $X$ is weakly (strongly) infine-dimensional if and only if $C(X)$ has weakly (strongly) infinite real rank. Some other properties of this concept are also investigated. In particular, we show that the group $C^{\ast}$-algebra $C^{\ast}({\mathbb F}_{\infty})$ of the free group on countable number of generators has strongly infinite real rank.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
