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研究生:蔡宗彣
研究生(外文):Chung-Wen Tsai
論文名稱:維度與整擴張
論文名稱(外文):Dimensions and Integral Extensions
指導教授:黃毅青
指導教授(外文):Ngai-Ching Wong
學位類別:碩士
校院名稱:國立中山大學
系所名稱:應用數學系研究所
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2004
畢業學年度:92
語文別:英文
論文頁數:18
中文關鍵詞:整擴張拓樸穩定秩覆蓋維度維度
外文關鍵詞:integral extensioncovering dimensiontopological stable rankdimension
相關次數:
  • 被引用被引用:0
  • 點閱點閱:71
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  • 下載下載:5
  • 收藏至我的研究室書目清單書目收藏:0
最近,Dawson和Feinstein證明了一個交換的Banach代數的拓樸穩定秩是一的話,那它的 Banach 代數整擴張的拓樸穩定秩也是一。在這篇論文中,我們提供了這個命題的部分相反結果:如果一個交換的C*-代數的某個Arens-Hoffman擴張的拓樸穩定秩是一的話,那這個C*-代數的拓樸穩定秩也是一。
Recently, Dawson and Feinstein showed that a Banach algebra integral extension B of a commutative
Banach algebra A of topological stable rank one is again of topological stable rank
one. In this thesis, we provide a partial converse to this statement: If an Arens-Hoffman extension
A® of a commutative C*-algebra A has topological stable rank one then A has topological
stable rank one.
Chapter 1: Introduction 1
Chapter 2: History and definition of dimensions 3
2.1 Historial remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2.2 Covering dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.3 Topological stable ranks . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Chapter 3: Results 11
3.1 Notations and preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3.2 Main results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
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[10] J. R. Munkres, Elements of Algebraic Topology, Addison-Wesley, 1984.
[11] J. R. Munkres, Topology, Prentice-Hall, Second Edition, 2000.
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