对抽象代数的哲学审视

The Study of Abstract Algebra from Philosophical Perspective

针对抽象代数中的几大重要代数系统,我们从代数系统建立的逻辑层次上得出抽象代数的本体是关系,从代数系统结构的同构意义上得出抽象代数的方法是同型,并从抽象代数的认识主体、理论结构、分析方法、物理意义四个层面分析了蕴涵在抽象代数中的科学美与真理性,进而还原了抽象代数的最深刻的人文意义。

After a careful study of several major algebraic systems in abstract algebra, we come to the conclusion that relation is the noumenon of abstract algebra taking into consideration their established logical levels, and that homotype is the research method considering their structured isomorphic meanings. The paper further analyzes the scientific beauty and truth implicated in abstract algebra from four aspects, namely, cognitive subject, theoretical structure, methodology, and physical significance, aiming to reduce the most profound humanistic significance of abstract algebra in the end.