检索规则说明:AND代表“并且”;OR代表“或者”;NOT代表“不包含”;(注意必须大写,运算符两边需空一格)
检 索 范 例 :范例一: (K=图书馆学 OR K=情报学) AND A=范并思 范例二:J=计算机应用与软件 AND (U=C++ OR U=Basic) NOT M=Visual
机构地区:[1]西北大学数学与科学史研究中心,陕西西安710127
出 处:《西北大学学报(自然科学版)》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)
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.
正在载入数据...
正在载入数据...
正在载入数据...
正在载入数据...
正在载入数据...
正在载入数据...
正在载入数据...
正在链接到云南高校图书馆文献保障联盟下载...
云南高校图书馆联盟文献共享服务平台 版权所有©
您的IP:18.189.186.244