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Studies in the History of Natural Sciences  2019, Vol. 38 Issue (4): 479-495    DOI:
ARTICLES     
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
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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     
Received: 02 May 2018      Published: 18 June 2022
ZTFLH:  N091  
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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.

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

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