早期p进数理论的历史发展

The early history of p-adic number theory

目的探讨早期p进数理论的产生和发展。方法文献考证与概念分析,主要通过亨塞尔(K.Hensel,1861—1941)和弗兰克尔(A.H.Fraenkel,1891—1965)的工作来解析p进数理论的思想。结果 p进数理论是亨塞尔发明的一种具体的域的理论,弗兰克尔对p进数理论进行了公理化,从而建立起了结构严谨的理论。结论早期的p进数理论是19世纪数学观念变革中的一个重要组成部分,不但对一般的域以及抽象代数学的产生和发展有重要影响,而且为代数数论等学科的发展注入了新的内涵和活力。

Ahn To discuss the early history of p-adic number theory. Methods Document research and concept analyzing, especially the analysis of the idea of Hensel（ 1861-1941 ） and Fraenkel（ 1891-1965 ）. Results p-adic number theory is the concrete field theory invented by Hensel. Fraenkel made it axiomatically mature. Conclusion p-adic number theory was an important part of the maths idology evolution in the change of the 19th century, which promoted the development of general field and abstract algebra. Simultaneously it encouraged the development of algebraic number theory.