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系統識別號 U0026-0907201515091900
論文名稱(中文) 關於Koethe猜想之整理
論文名稱(英文) A taxonomy of Koethe's problem
校院名稱 成功大學
系所名稱(中) 數學系應用數學碩博士班
系所名稱(英) Department of Mathematics
學年度 103
學期 2
出版年 104
研究生(中文) 劉顯倫
研究生(英文) Hin-Lon Lao
學號 L16025018
學位類別 碩士
語文別 英文
論文頁數 22頁
口試委員 口試委員-黃柏嶧
口試委員-陳家駒
指導教授-柯文峰
中文關鍵字 Koethe猜想 
學科別分類
中文摘要 在1930年,數學家Gottfried Maria Hugo Köthe提出了一個在環論上的問題,今天我們稱之為Koethe猜想。在本篇論文中,我們將探討數學家們在這個問題上所取得的進展。
英文摘要 In this paper we compile the results and problems related to the Koethe's problem in ring theory. Each section is devoted to an approach or a perspective toward the problem. Contents in distinct sections may be related, or independent.
論文目次 Background 6
Koethe's problem 7
1.Levitzke's three problems and Koethe's problem 7
2.Levitzke's second problem and Kurosch's problem 9
3.Amitsur's condition on dimension of algebra 10
4.Amitsur's theorem and Krempa's formulation 11
5.Group of automorphisms of ring 12
6.Koethe's subset 12
7.Brown-Mccoy radical 13
8.Behrens radical 14
9.Andrunakievich's chain 16
Andrunakievich's problem 16
10.Rings which are sums of two subrings 17
11.Tensor product of algebras 18
12.Special classes of algebras and rings 19
References 21
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