试论由不变量论到交换环论的思想嬗变  

On the Evolution of the Thought from Invariant Theory to Commutative Ring Theory

作　　者：王淑红[1] WANG Shu-hong(School of Mathematical Science,Hebei Normal University,Shijiazhuang 050024,China)

机构地区：[1]河北师范大学数学科学学院,石家庄050024

出　　处：《科学技术哲学研究》2021年第4期93-97,共5页Studies in Philosophy of Science and Technology

基　　金：国家自然科学基金资助项目“代数数论及其相关领域的历史研究”(11871018)。

摘　　要：不变量论是交换环论的主要来源之一。在其产生、发展、成熟到批判的过程中,已经孕育了交换环论的素材和思想。通过文献分析和概念考证,试图说明不变量论是如何通向交换环论的。结果表明希尔伯特的有限基定理在这一过程中发挥了关键作用,不但使得数学思维方式发生转变,由构造性证明转变为存在性证明,而且使得不变量论直接通向交换环论。Invariance theory is one of the main sources of commutative ring theory.In the process of its creation,development,maturity and critique,the material and ideas of commutative ring theory had been nurtured.Through literature analysis and conceptual research,how invariance theory lead to commutative ring theory was explained.The results show that Hilbert’s finite basis theorem played a key role in this process,which not only changed the mathematical way of thinking from constructive proof to existential proof,but also directly lead the invariant theory to commutative ring theory.

关 键 词：交换环 不变量 有限基定理 升链条件 

分 类 号：N09[自然科学总论—科学技术哲学]