Preface to the Second Edition
Preface to the First Edition
To the Reader
Domains and Fields
Homomorphisms and Ideals
Polynomial Rings over Fields
Prime Ideals and Maximal Ideals
The Galois Group
Roots of Unity
Solvability by Radicals
Independence of Characters
The Fundamental Theorem of Galois Theory
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] epub pdf mobi txt 下载
伽罗瓦理论（第2版）（英文版） [Galois Theory 2nd ed] 下载 epub mobi pdf txt