$H^\infty_\R(\D)$和$A_\R(\D)$的低稳定秩和拓扑稳定秩
The Bass and Topological Stable Ranks of $H^\infty_\R(\D)$ and $A_\R(\D)$
摘要：
本文证明了$H^\infty_\R(\D)$的Bass稳定秩为2.这证明了S.特瑞尔我们用两种不同的方法来实现这一点，一种是直接证明，另一种是首先证明$H^\infty_\R(\D)$的拓扑稳定秩是2。应用这些结果给出了R. Rupp和A. Sasane指出$A_\R(\D)$的Bass稳定秩是2，$A_\R(\D)$的拓扑稳定秩是2，解决了第二作者的一个猜想。我们还提出了一个$\bar\partial$ -自由证明的第二作者的特征的可约对$A_\R(\D)$。
英文摘要：
In this note we prove that the Bass stable rank of $H^\infty_\R(\D)$ is two. This establishes the validity of a conjecture by S. Treil. We accomplish this in two different ways, one by giving a direct proof, and the other, by first showing that the topological stable rank of $H^\infty_\R(\D)$ is two. We apply these results to give new proofs of results by R. Rupp and A. Sasane stating that the Bass stable rank of $A_\R(\D)$ is two and the topological stable rank of $A_\R(\D)$ is two, settling a conjecture by the second author. We also present a $\bar\partial$-free proof of the second author's characterization of the reducible pairs in $A_\R(\D)$.
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。
