科学技术哲学研究
科學技術哲學研究
과학기술철학연구
Science Technology and Dialectics
2014年
5期
92~97
,共null页
对偶群 格 戴德金 奥尔 数学结构
對偶群 格 戴德金 奧爾 數學結構
대우군 격 대덕금 오이 수학결구
dual group ; lattice ; R. Dedekind ; 0. Ore ; mathematical structure
格论是结构数学的重要组成部分,是结构数学研究的典型范例,溯源于戴德金的对偶群,后经奥尔的发展成为抽象数学结构。但它在诞生伊始并未如群、环、域等代数结构那样受到重视,其历史研究也很薄弱。伴随近年来格论的自身发展及其应用的逐步展开,其历史研究价值渐趋凸显。通过对格论的早期历史进行探源和分析,试图厘清格论早期发展的思想线索,为结构数学的研究提供新的素材和思想。
格論是結構數學的重要組成部分,是結構數學研究的典型範例,溯源于戴德金的對偶群,後經奧爾的髮展成為抽象數學結構。但它在誕生伊始併未如群、環、域等代數結構那樣受到重視,其歷史研究也很薄弱。伴隨近年來格論的自身髮展及其應用的逐步展開,其歷史研究價值漸趨凸顯。通過對格論的早期歷史進行探源和分析,試圖釐清格論早期髮展的思想線索,為結構數學的研究提供新的素材和思想。
격론시결구수학적중요조성부분,시결구수학연구적전형범례,소원우대덕금적대우군,후경오이적발전성위추상수학결구。단타재탄생이시병미여군、배、역등대수결구나양수도중시,기역사연구야흔박약。반수근년래격론적자신발전급기응용적축보전개,기역사연구개치점추철현。통과대격론적조기역사진행탐원화분석,시도전청격론조기발전적사상선색,위결구수학적연구제공신적소재화사상。
As an important part of structural mathematics, lattice theory is a typical example of historical study of structural mathematics. It mainly originated from R. Dedekind' s dual group, and developed into a mathematical structure after O. Ore. But at the beginning, it wasn' t so significant as group, ring, field and other algebraic struc- tures, so its historical study was very weak. With its development and application in recent years, its value of histori- cal research is highlighted. Based on the early history of lattice theory, this paper outlines its development, and pro- vides valuable materials and thoughts for the study of structure mathematics.