摘要
环论是抽象代数学中最为深刻的部分之一,亦是结构数学的重要分支。它起源于19世纪早期,到20世纪二三十年代形成严谨的结构化体系。对环论历史研究,进行不同角度的考察。从思想史角度探讨环论概念的发展,掌握环论与其他相关分支和学科之间的关系,认识在环论发展过程中起主导作用的集合论、公理化、抽象化、结构化等思想,同时从数学文化史的角度,探讨数学家之间的师承关系及其对数学思想的影响。
Ring theory is one of the most profound parts of modern abstract algebra, constituting an important branch of structural mathematics. Having stemmed from the early 19 century mathematical analysis, it developed into a rigorous structural system in the 1920 - 30s. Several approaches are suggested for the study of the history of the ring theory. From the point of view of intellectual history, the evolution of the concept of ring is analyzed, the relationship between the ring theory and other related branches and subjects is investigated, and the leading roles of the set theory, axiomatization, abstract and structuring thought in this development are comprehended. From the perspective of sociology of scientific knowledge and mathematical culture, the mathematical community which con- tributes to the development of the ring theory is considered, with a particular focus on the teacher - student relation- ship and its influence on mathematical thinking.
出处
《科学技术哲学研究》
CSSCI
北大核心
2017年第2期80-85,共6页
Studies in Philosophy of Science and Technology
基金
国家自然科学基金资助项目(11401161
11671117)
河北省自然科学基金资助项目(A2014205055)
河北省高校百名优秀创新人才支持计划
关键词
环论
集合论
公理化
结构化
数学家群体
ring theory
set theory
axiomatization
structuring
mathematical community
