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自然科学史研究  2019, Vol. 38 Issue (4): 479-495    
论文     
对埃米尔·阿廷《伽罗瓦理论》的历史分析
张勇1, 邓明立2
1.北京大学哲学系,北京 100871;
2.河北师范大学数学与信息科学学院,石家庄 050024
A Historical Analysis of Emil Artin's Galois Theory
ZHANG Yong1, DENG Mingli2
1. Department of Philosophy, Peking University, Beijing 100871, China;
2. College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang, Hebei 050024, China
 全文: PDF(1356 KB)  
摘要： 用抽象代数来处理伽罗瓦理论由阿廷完成,他重视线性代数方法,成功绕过本原元素定理而证明了伽罗瓦理论的基本定理。文章在已有研究的基础上,分析了阿廷成功解读伽罗瓦理论的多种因素及其著作《伽罗瓦理论》的背景、结构及定位。在伽罗瓦理论的抽象化历程中,阿廷受到戴德金、希尔伯特、施泰尼茨等人的影响,这说明代数学在19世纪和20世纪发展环境的变化是阿廷《伽罗瓦理论》成功的前提。最后,文章调查了《伽罗瓦理论》对现代伽罗瓦理论专著及代数学教材的影响。
关键词： 伽罗瓦;  《伽罗瓦理论》;  阿廷    
Abstract: Emil Artin(1898—1962) reformulated Galois theory via abstract algebra. He linearized the theory, and succeeded in bypassing the primitive element theorem to prove its fundamental theorem. On the basis of predecessors' research, this paper analyses the various factors that led to Artin's successful reinterpretation of Galois theory, and further elaborates on the background, structure and role of his book Galois Theory. It provides an in-depth understanding about how Artin was influenced by Dedekind, Hilbert and Steinitz on the abstract process of Galois theory. It further reveals that the elevation of the level of abstraction inalgebra between the 19th and 20th centuries was a prerequisite for the success of Artin's Galois Theory. Finally, the author investigates the influence of Galois Theory on modern Galois theory monographs and algebra textbooks. This paper also commemorates the 120th anniversary of the birth of Emil Artin.
Key words: Galois    Galois Theory    Emil Artin
收稿日期: 2018-05-02 出版日期: 2022-06-18
ZTFLH:  N091  
基金资助: 国家自然科学基金资助项目"群论统一数学的历史研究"(项目编号:11671117)、"代数数论及其相关领域的历史研究(项目编号:11871018)
通讯作者: 邓明立,1962年生,河北辛集人,教授,研究方向为代数学及近现代数学史。   
作者简介: 张勇,1990年生,河北邢台人,北京大学数学科学学院与哲学系联合培养博士研究生,研究方向为拓扑学及近现代数学史。
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引用本文:

张勇, 邓明立. 对埃米尔·阿廷《伽罗瓦理论》的历史分析[J]. 自然科学史研究, 2019, 38(4): 479-495.

ZHANG Yong, DENG Mingli. A Historical Analysis of Emil Artin's Galois Theory. Studies in the History of Natural Sciences, 2019, 38(4): 479-495.

链接本文:

http://www.shns.ac.cn/CN/    或    http://www.shns.ac.cn/CN/Y2019/V38/I4/479

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