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Rank preserving in integral extensions of commutative c^*-algebras

Chung-Wen Tsai Ngai-Ching Wong

Functional Analysis mathscidoc:1910.43772

Taiwanese Journal of Mathematics, 16, (2), 545-553, 2012
Let A , A be two regular commutative unital Banach algebras such that A is integral over A . In 2003, Dawson and Feinstein showed that the topological stable rank A whenever A . In this note, we investigate whether we will have A in general. For instance, when A is a commutative unital A -algebra, we show that A , and the equality holds at least when the integral extension is separable. In general, A and A have the same Bass stable ranks A .
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@inproceedings{chung-wen2012rank,
  title={RANK PRESERVING IN INTEGRAL EXTENSIONS OF COMMUTATIVE C^*-ALGEBRAS},
  author={Chung-Wen Tsai, and Ngai-Ching Wong},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020213547687932301},
  booktitle={Taiwanese Journal of Mathematics},
  volume={16},
  number={2},
  pages={545-553},
  year={2012},
}
Chung-Wen Tsai, and Ngai-Ching Wong. RANK PRESERVING IN INTEGRAL EXTENSIONS OF COMMUTATIVE C^*-ALGEBRAS. 2012. Vol. 16. In Taiwanese Journal of Mathematics. pp.545-553. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020213547687932301.
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