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关键词：
Galois Theory
书目信息
ISBN：
9780387287256（13位）
中图分类号：
O1
杜威分类号：
中文译名：
伽罗瓦理论
作者：
Steven H. Weintraub
编者：
语种：
English
出版信息
出版社：
Springer
出版地：
出版年：
2006
版本：
版本类型：
原版
丛书题名：
Universitext
卷期：
文献信息
关键词：
Mathematics
前言：
摘要：
内容简介：
<P>Classical Galois theory is a subject generally acknowledged to be one of the most central and beautiful areas in pure mathematics. This text develops the subject systematically and from the beginning, requiring of the reader only basic facts about polynomials and a good knowledge of linear algebra. </P> <P>Key topics and features of this book:</P> <P>- Approaches Galois theory from the linear algebra point of view, following Artin</P> <P>- Develops the basic concepts and theorems of Galois theory, including algebraic, normal, separable, and Galois extensions, and the Fundamental Theorem of Galois Theory</P> <P>- Presents a number of applications of Galois theory, including symmetric functions, finite fields, cyclotomic fields, algebraic number fields, solvability of equations by radicals, and the impossibility of solution of the three geometric problems of Greek antiquity</P> <P>- Excellent motivaton and examples throughout</P> <P>The book discusses Galois theory in considerable generality, treating fields of characteristic zero and of positive characteristic with consideration of both separable and inseparable extensions, but with a particular emphasis on algebraic extensions of the field of rational numbers. While most of the book is concerned with finite extensions, it concludes with a discussion of the algebraic closure and of infinite Galois extensions.</P> <P>Steven H. Weintraub is Professor and Chair of the Department of Mathematics at Lehigh University. This book, his fifth, grew out of a graduate course he taught at Lehigh. His other books include <STRONG>Algebra: An Approach via Module Theory</STRONG> (with W. A. Adkins).</P>
目次：
<P>Introduction to Galois Theory.- Field Theory and Galois Theory.- Development and Applications of Galois Theory.- Extensions of the Field of Rational Numbers.- Further Topics in Field Theory.- A. Some Results from Group Theory.- B. A Lemma on Constructing Fields.- C. A Lemma from Elementary Number Theory.- References.- Index. </P>
附录：
全文链接：
读者对象：
Grad. textbook
实体信息
页码：
184
装帧：
Soft
尺寸：
其它形态细节：
其它信息
原价：
EUR
42.9500
原版ISBN：
其它ISBN：
图书特色：
书评：
扩展信息
Isbn：
0387287256
issue：
2006JC02
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