摘要
伽罗瓦关于代数方程求解的工作被视为现代代数学的起点,但他的工作以晦涩而难以理解。通过对伽罗瓦原始文献的分析讨论,发现若以因式分解的数学思想为切入点,则伽罗瓦工作的最核心部分是建立起了因式分解与群分解的对应关系。因式分解的过程实质上是方程的系数域不断扩张的过程,伽罗瓦利用这一过程产生的方程的群的分解来反映这种扩张,使得对方程的研究变为了对群的研究,从而开启了19世纪代数学革命的序幕。
Galois＇s work for solving the algebraic equations is deemed as the beginning of Modern Algebra. It is dif- ficult to follow Galois＇s idea from his obscure transcript. After analyzing the memoir of Galois, it is found that if ap- plying the mathematic thought of factorization as the entry point, then the core of Galois＇s work is the correspon- dence between factorization and the decomposition of the group. The process of factorization in fact is the process for keeping expanding the coefficient domains of the equation. Galois used the decomposition of the group of equation which is produced by the factorization to describe this process of expansions. This view point changed the object of study from equation to group, opened the door of the revolution of the algebra in 19th century.
出处
《西北大学学报（自然科学版）》
CAS
CSCD
北大核心
2013年第6期1005-1010,共6页
Journal of Northwest University（Natural Science Edition）
基金
国家自然科学基金资助项目(11171271
11326048)
关键词
伽罗瓦
因式分解
方程的群
Galois
factorization
the group of equation
