Field and Galois Theory Morandi, Patrick (New Mexico State University, Las Cruces, NM, USA)(著/文) - Springer-Verlag New York Inc.
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Field and Galois Theory
- 初版年月日
- 2011-09-17
- 登録日
- 2018年6月10日
- 最終更新日
- 2018年6月10日
紹介
The purpose of this book is twofold. First, it is written to be a textbook for a graduate level course on Galois theory or field theory. Second, it is designed to be a reference for researchers who need to know field theory. The book is written at the level of students who have familiarity with the basic concepts of group, ring, vector space theory, including the Sylow theorems, factorization in polynomial rings, and theorems about bases of vector spaces. This book has a large number of examples and exercises, a large number of topics covered, and complete proofs given for the stated results. To help readers grasp field.
目次
I Galois Theory.- 1 Field Extensions.- 2 Automorphisms.- 3 Normal Extensions.- 4 Separable and Inseparable Extensions.- 5 The Fundamental Theorem of Galois Theory.- II Some Galois Extensions.- 6 Finite Fields.- 7 Cyclotomic Extensions.- 8 Norms and Traces.- 9 Cyclic Extensions.- 10 Hubert Theorem 90 and Group Cohomology.- 11 Kummer Extensions.- III Applications of Galois Theory.- 12 Discriminants.- 13 Polynomials of Degree 3 and 4.- 14 The Transcendence of ? and e.- 15 Ruler and Compass Constructions.- 16 Solvability by Radicals.- IV Infinite Algebraic Extensions.- 17 Infinite Galois Extensions.- 18 Some Infinite Galois Extensions.- V Transcendental Extensions.- 19 Transcendence Bases.- 20 Linear Disjointness.- 21 Algebraic Varieties.- 22 Algebraic Function Fields.- 23 Derivations and Differentials.- Appendix A Ring Theory.- 1 Prime and Maximal Ideals.- 2 Unique Factorization Domains.- 3 Polynomials over a Field.- 4 Factorization in Polynomial Rings.- 5 Irreducibility Tests.- Appendix B Set Theory.- 1 Zorn's Lemma.- 2 Cardinality and Cardinal Arithmetic.- Appendix C Group Theory.- 1 Fundamentals of Finite Groups.- 2 The Sylow Theorems.- 3 Solvable Groups.- 4 Profinite Groups.- Appendix D Vector Spaces.- 1 Bases and Dimension.- 2 Linear Transformations.- 3 Systems of Linear Equations and Determinants.- 4 Tensor Products.- Appendix E Topology.- 1 Topological Spaces.- 2 Topological Properties.- References.
上記内容は本書刊行時のものです。
