伽羅瓦對(duì)應(yīng)導(dǎo)論

內(nèi)容概要

埃瓦里斯特·伽羅華是法國(guó)對(duì)函數(shù)論、方程式論和數(shù)論作出重要貢獻(xiàn)的數(shù)學(xué)家，他的工作為群論奠定了基礎(chǔ)；在父親自殺后，他放棄投身于數(shù)學(xué)生涯，注冊(cè)擔(dān)任輔導(dǎo)教師，結(jié)果因撰寫反君主制的文章而被開除，且因信仰共和體制而兩次下獄。伽羅華死于一次近乎自殺的決斗，引起了后人的種種猜測(cè)。可能是被?；逝苫蚓剿づ拢瑫r(shí)年21歲。他被公認(rèn)為是數(shù)學(xué)史上兩個(gè)最具浪漫主義色彩的人物之一。
這本《伽羅瓦對(duì)應(yīng)導(dǎo)論(第2版)》是英文版。

書籍目錄

Preface
Chapter I.Preliminaries-Groups and Rings
1. Introduction to Groups
2. Quotient Groups and Sylow Subgroups
3. Finite Abelian Groups and Solvable Groups
4. Introduction to Rings
5. Factoring in F[x]
Chapter II. Field Exteio
1. Simple Exteio
2. Algebraic Exteio
3. Splitting Fields and Normal Exteio
Chapter III. The Galois Correspondence
1. The Fundamental Correspondence
2. The Solvable Correspondence
Chapter IV. Applicatio
1. Cotructibility
2. Roots of Unity
3. Wedderburn's Theorem
3. Dirichlet's Theorem and Finite Abelian Groups
Appendix A - Groups
1. Group Actio and the Sylow Theorems
2. Free Groups, Generato and Relatio
Appendix B - Factoring in Integral Domai
1. Euclidean Domai and Principal Ideal Domai
2. Prime and Irreducible Elements
3. Unique Factorization Domai
Appendix C - Vector Spaces
1. Subspaces, Linear Independence and Spanning
2. Bases and Dimeion
Bibliogr

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