结构数学视域下抽象代数的崛起与扩散  

The Rise and Spread of Abstract Algebra from the Perspective of Structural Mathematics

作　　者：闫焱 YAN Yan(College of Science,North China University of Science and Technology,Tangshan,Hebei,063210)

机构地区：[1]华北理工大学理学院,河北唐山063210

出　　处：《自然辩证法通讯》2025年第2期76-82,共7页Journal of Dialectics of Nature

基　　金：国家自然科学基金资助项目“结构数学在现代代数学中的渗透与应用”(项目编号:12171137)。

摘　　要：代数学作为现代数学重要的基础与核心,伴随着结构数学的兴起,经历了从经典的符号演算到抽象代数的发展历程。抽象代数主要研究各种公理化代数系统和不同代数系统之间的相互联系,并以其结构的一般性,实现了将许多种类各异的、高度数学化的学科进行代数化处理。本文在结构数学的视域下,分析了抽象代数如何从古典代数经历了对象化,集合化,结构形式化的过程。揭示了在20世纪交叉融合背景下,抽象代数通过将其思想和方法渗入到其他学科领域中,从而推动了诸多交叉学科的发展。As an important foundational core of modern mathematics,algebra has developed from classical symbolic calculus to abstract algebra with the rise of structural mathematics.Abstract algebra mainly studies the relations between various axiomatic algebraic systems and different algebraic systems,and enables algebraic treatment of many different and highly mathematical disciplines with its general structure.In the view of structural mathematics,this paper analyzes how abstract algebra underwent objectification,collectivization and structural formalization from classical algebra.It is revealed that abstract algebra has promoted the development of many interdisciplinary disciplines by introducing its ideas and methods into other disciplines against the background of cross fusion in the 20th century.

关 键 词：结构数学 代数学 抽象代数 交叉融合 

分 类 号：O15[理学—数学] N09[理学—基础数学]