斯坦尼兹1910年抽象域论工作的历史分析

E. Steinitz's Work on the Theory of Abstract Field in 1910

斯坦尼兹是19世纪末20世纪初德国最伟大的代数学家之一,也是抽象域论研究的主要奠基人。他的《域的代数理论》(1910)是代数学史上划时代的经典文献,揭开了域论抽象研究的序幕,是后来许多数学家进行代数学结构研究的基础。在对原始文献进行仔细研究的基础上,探讨了斯坦尼兹从事抽象域论研究的主要原因,着重分析了其文献中涉及的具体研究内容以及对未来几十年间代数学研究的影响。

E. Steinitz is one of the most i,dluential mathematicians in Germany at the turn of the 19th and 20th centuries, as well as the main founder of the theory of abstract field. His work ＂Algebraische Theorie der Krper＂ （1910） is described as the classic literature in the history of algebra, which indicated the beginning of the research on the theory of abstract field. It is also the basis of the research on algebraic structure. On the basis of the classified researches of primary sources, this paper discusses the reasons why E. Steinitz was engaged in the research on the theory of abstract field, analyzes his above-mentioned work in detail and reviews its historical impact on mathe- matical research in the coming decades.