对埃米尔·阿廷《伽罗瓦理论》的历史分析

A Historical Analysis of Emil Artin’s Galois Theory

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。

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 19 th and 20 th 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 120 th anniversary of the birth of Emil Artin.