非交换环论的早期实践基础与理论构建

The Practical Foundation and Theoretical Construction of Early Noncommutative Ring Theory

非交换环论是环论的重要组成部分之一。它起源于四元数、外代数、群代数、矩阵等一些具体的案例,其后数学家们对这些案例进行整合和思想升华,进行分类和结构研究,构建出了非交换环论,对现代数学的发展产生了举足轻重的影响。通过文献考证与概念分析,对早期非交换环论的实践基础与理论构建进行历史分析,探索早期非交换环论进入一个个新境地的里程碑和决定因素。

Noncommutative ring theory is one of the important components of the ring theory. It originated from some specific cases such as quaternion,external algebra,group algebra,matrix,etc. Later,mathematicians integrated the thought of these cases,carried out classification and structure research,and constructed the noncommutative ring theory. It has had significant impacts on the modern mathematics. Through literature research and conceptual analysis,the practical foundation and the theoretical construction of the early noncommutative ring theory were analyzed,and its milestones and determinants of entering a new situation were explored.