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研究生: 劉顯倫
Lao, Hin-Lon
論文名稱: 關於Koethe猜想之整理
A taxonomy of Koethe's problem
指導教授: 柯文峰
Ke, Wen-Fong
學位類別: 碩士
Master
系所名稱: 理學院 - 數學系應用數學碩博士班
Department of Mathematics
論文出版年: 2015
畢業學年度: 103
語文別: 英文
論文頁數: 22
中文關鍵詞: Koethe猜想
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  • 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。

    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.

    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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