伽罗瓦理论（第2版）（英文版） [Galois Theory 2nd ed] 下载 mobi epub pdf 电子书 2025

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内容简介

　　《伽罗瓦理论(第2版)(英文版)》是第二版，较一版有很大的改进。证明更加清晰、详尽。由于多变形对称群和多项式的Galois群的相似性，书中以平面上的多边形对称群为开始。这种相似性可以帮助读者理解书中的有关理论知识。书中也包含了一些新的定理，例如：不可约情形。书中用完整的证明和大量练习清晰、有效地讲述了Galois理论。包括：立方、四次方公式的Galois理论的基本理论；五次Galois大定理的不可解性；立方和四次方Galois群的计算。补充了群论、尺规结构和Galois的早期历史。《伽罗瓦理论(第2版)(英文版)》是一本Galois理论简明教程，很适合研究生一年级作为教材学习；也是一本很理想的课外学习书。目次：对称；环；同态和理想；商环；域上的多项式环；素理想和大理想；不可约多项式；经典多项式；分裂域；Galois群；单位根；根式可解性；特征的独立性；Galois扩张；Galois理论的基本定理；应用；Galois大定理；判别式；二次、三次、四次多项式的Galois群；结尾。

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目录

Preface to the Second Edition
Preface to the First Edition
To the Reader
Symmetry
Rings
Domains and Fields
Homomorphisms and Ideals
Quotient Rings
Polynomial Rings over Fields
Prime Ideals and Maximal Ideals
Irreducible Polynomials
Classical Formulas
Splitting Fields
The Galois Group
Roots of Unity
Solvability by Radicals
Independence of Characters
Galois Extensions
The Fundamental Theorem of Galois Theory

前言/序言

　　There are too many errors in the first edition， and so a "corrected nth printing" would have been appropriate. However， given the opportunity to makechanges， I felt that a second edition would give me the flexibility to changeany portion of the text that I felt I could improve. The first edition aimedto give a geodesic path to the Fundamental Theorem of Galois Theory，and I still think its brevity is valuable. Alas， the book is now a bit longer，but I feel that the changes are worthwhile. I began by rewriting almost allthe text， trying to make proofs clearer， and often giving more details thanbefore. Since many students find the road to the Fundamental Theoreman intricate one， the book now begins with a short section on symmetrygroups of polygons in the plane; an analogy of polygons and their symmetry groups with polynomials and their Galois groups can serve as a guideby helping readers organize the various definitions and constructions. Theexposition has been reorganized so that the discussion of solvability byradicals now appears later; this makes the proof of the Abel-Ruffini theorem easier to digest. I have also included several theorems not in the firstedition. For example， the Casus Irreducibilis is now proved， in keepingwith a historical interest lurking in these pages.
　　I am indebted to Gareth Jones at the University of Southampton who，after having taught a course with the first edition as text， sent me a detailed list of errata along with perspicacious comments and suggestions. Ialso thank Evan Houston， Adam Lewenberg， and Jack Shamash who madevaluable comments as well. This new edition owes much to the generosityof these readers， and I am grateful to them.

伽罗瓦理论（第2版）（英文版） [Galois Theory 2nd ed] 下载 mobi epub pdf txt 电子书 格式

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物流满意，商品给力，对于京东服务，一直十分好评！

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很不错！物流也很快！

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伽罗华理论中的经典之一

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超级好的东西，很好用，下次还来买，很满意。

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经过两个多世纪，一些著名的数学家，如欧拉、旺德蒙德、拉格朗日、鲁菲尼等，都做了很多工作，但都未取得重大的进展。19世纪上半叶，阿贝尔受高斯处理二项方程 (p为素数)的方法的启示，研究五次以上代数方程的求解问题，终于证明了五次以上的方程不能用根式求解。他还发现一类能用根式求解的特殊方程。这类方程现在称为阿贝尔方程。阿贝尔还试图研究出能用根式求解的方程的特性，由于他的早逝而未能完成这项工作。伽罗瓦理论还特别对尺规作图问题给出完全的刻画。人们已经证明：这种作图问题可归结为解有理数域上的某些代数方程。这样一来，一个用直尺和圆规作图的问题是否可解，就转化为研究相应方程的伽罗瓦群的性质。

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经典中的经典经典中的经典经典中的经典经典中的经典

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书很好，速度也很快，专业书籍值得一阅

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