摘要
鉴于多项式环在现代数学中的重要性以及数学史上的关键地位,运用数学概念史研究的方法,探寻多项式环概念建立和发展的历史过程。研究发现:首先,通过诺特、范德瓦尔登等数学家的奠基工作,多项式环从具体特例中抽象出来,一般化的多项式环概念最终得以建立。其次,代数学家雅各布森对多项式环概念的发展,经历了从未定元向超越元的认识变迁,他在前人研究的基础上,进一步揭示出多项式环的序列形式和超越本质。历史意蕴在于:多项式环概念的确立拓展了多项式的内涵,打破了多项式与函数以往混为一谈的局面;多项式环的概念史反映了代数学发展中代数倾向的学科魅力和高度抽象的理论精神,显现出数学史的连续性。
Given the importance of polynomial rings in modern mathematics and their fundamental role in the history of mathematical thought,this study applies the methodology of conceptual history to trace the formation and development of the concept of polynomial rings.It is found that the generalized concept of polynomial rings was gradually established through the foundational work of mathematicians such as Emmy Noether and Bartel van der Waerden,who abstracted the concept from specific instances.In addition,the algebraist Nathan Jacobson contributed significantly to its conceptual evolution by shifting the focus from indeterminate to transcendental indeterminate.Building upon earlier research,he further clarified the sequential form and transcendental nature of polynomial rings.The historical significance lies in the fact that the formalization of the concept broadened the scope of the concept of polynomials and broke with the earlier tendency to confuse polynomials with functions.The conceptual history of polynomial rings not only reflects the algebraic focus and high level of abstraction in the development of modern algebra but also highlights the continuity inherent in the history of mathematics.
作者
杨保强
YANG Baoqiang(School of Mathematics and Computer Science,Yan′an University,Yan′an 716000,Shaanxi,China)
出处
《内蒙古师范大学学报(自然科学版)》
2025年第4期375-380,共6页
Journal of Inner Mongolia Normal University(Natural Science Edition)
基金
延安大学博士科研启动资金资助项目“本原方程的历史研究”(YDBK2022-64)。
关键词
多项式环
代数学
数学概念史
数学史
polynomial ring
algebra
history of mathematical concept
history of mathematics
