Some Historical Notes On/Artin's Galoissche Theorie

Galois theory is a brilliant part of algebra.As an Austria mathematician,Emil Artin has made outstanding contribution to its continuous improvement throughout the process.At the beginning of 20th century,as one of representatives of the German algebra school,Artin absorbed the mathematic thinking of Dedekind,Hilbert and Steinitz,he reconstructed the classical galois theory with the language of modern algebra and the viewpoint of field theory.In 1926,Artin established an algebra seminar at the university of Hamburg,he explained the field theory and galois theory to Van der Waerden with the strict,clear and graceful mathematical language,the corresponding content appeared in the "Modern Algabra" of Van der Waerden series in 1930.In 1942 and 1946,Artin published a book named "Galois Theory"in English,then he published it in German in 1959 aseparately.All these books have made the galois theory a part of the modern algebra,and improved the galois theory as a separate advanced mathematics textbook in mathematical education.This book has inspired the vitality of galois theory,and promoted the rapid development of galois theory for a long time.Some people say that "Galois Theory" makes Artin become a master of galois theory,I think it has a close relationship with the contribution which Artin had made in algebra,algebraic number theory and class field theory in the early 20th century.The development of ion during that period provided Artin a powerful mathematical tool.In this paper,I conduct a systematic analysis about the content of "Galois Theory" in 1959 and research the impact of all the three editions in history on the basis of a large number of historical documents.The main results:1.This dissertation describes the background of Artin's book "Galoissche Theorie".Because of Artin's interest in mathematics,his academic experiences,the impact of previous researches,this book appeared in the environment of the abstraction of field theory.I analyse the history factors of this book's appearance and the necessity about Artin's reconstruction of galois theory,then attempt to explain the ins and outs about this book in the history.2.This dissertation induces the writing features and summarizes unique aspects during the research about the content of this book,emphasizes and explains the unique places in the the content arrangement.3.This dissertation analyses the sources of mathematical thought which is not mentioned in this book,describes how does the thought of Dedekind,Hilbert and Steinitz influence Artin's idea about galois theory,and how does Artin improve the galois theory with the method of abstract algebra,on the basis of the deep understanding of predecessors's mathematical ideas.This means that Artin's galois theory has a significant impact in history.4.This dissertation collects and analyses some modern books about galois theory to indicate that this book has a profound impact on later researchers and teaching materials,it means Emil Artin is a master in the development of galois theory.