《Field and Galois Theory》是2020年世界圖書出版公司出版的圖書。
基本介紹
- 外文名:Field and Galois Theory
- 作者:Patrick Morandi
- 出版時間:2020年
- 出版社:世界圖書出版公司
- ISBN:9787506259552
- 開本:24 開
- 裝幀:平裝-膠訂

《Field and Galois Theory》是2020年世界圖書出版公司出版的圖書。
Field and Galois Theory 《Field and Galois Theory》是2020年世界圖書出版公司出版的圖書。P. Morandi,美國新墨西哥州立大學( New Mexico State University)數學科學系教授。
《Galois Theory》是1997年Dover Publications出版的圖書,作者是Emil Artin。內容簡介 Clearly presented elements of one of the most penetrating concepts in modern mathematics include discussions of fields, vector spaces, homogeneous linear equations, extension fields, polynomials, algebraic elements, as well ...
It is this latter that forms the topic of this book. Although its roots go back much further, the quest to understand symmetry really begins with the tragic young genius Evariste Galois, who died at the age of 20 in a duel. He used symmetry to understand algebraic equations, and he dis...
《抽象代數講義(第3卷)》是2000年世界圖書出版公司出版的圖書,作者是NathanJacobson。內容介紹 The present volume completes the series of texts on algebra which the author began more than ten years ago.圖書特點 The account of field theory and Galois theory which we give here is based on the ...
1.Field extensions 2.Algebraic quanities 3.Algebraic extensions 4.The characteristic of field 5.Separable and inseparable algebraic extensions 6.Splitting fields and normal extensions 7.The fundamental theorem of Galois theory 8.Galois fields 9.The theorem of the primitive element ……Ⅲ.IDEALS AND ...
6 Fields and Field Extensions 7 Galois Theory 8 Topology and Topological Spaces Algebraic Topology and the Final Proof Appendix A: A Version of Gauss's Original Proof Appendix B: Cauchy's Theorem Revisited Appendix C: Three Additional Complex Analytic Proofs of the Fundamental Theorem of Algebra A...
13.6 natural and accessory irrationalities 13.7 polynomial equations exercises part iii——the theory of binomials 14 binomials 14.1 irreducibility 14.2 the galois group of a binomial 14.3 the independence of irrational numbers exercises 15 families of binomials 15.1 the splitting field 15.2 ...
7.Field Theory 7.1 Fields and their Extensions 7.2 Splitting Fields 7.3 The Algebraic Closure of a Field 7.4 Separability 7.5 Automorphisms of Field Extensions 7.6 The Fundamental Theorem of Galois Theory 7.7 Roots of Unity 7.8 Finite Fields 7.9 Primitive Elements; Norm and Trace 7....
3.1 Field-Theoretic Algebraic Number Theory 3.1.1 Galois Theory 3.1.2 Number Fields 3.1.3 Examples 3.1.4 Characteristic Polynomial, Norm, Trace 3.1.5 Noether's Lemma 3.1.6 The Basic Theorem of Kummer Theory 3.1.7 Examples of the Use of Kummer Theory 3.1.8 Artin-Schreier Theory...
7.3 The Algebraic Closure of a Field 7.4 Separability 7.5 Automorphisms of Field Extensions 7.6 The Fundamental Theorem of Galois Theory 7.7 Roots of Unity 7.8 Finite Fields 7.9 Primitive Elements; Norm and Trace 7.10 Galois Theory of Equations 7.11 The Solution of Equations by ...
" [E2], Imade the reading of Galois original memoir a major part of my study of Galois theory, and I saw that the modern treatments of Galois theory lacked much of the simplicity and clarity of the original.
6.Differential Modules and Presentations Arithmetic Theory Chapter Ⅵ:Galois Cohomology 1.Cohomology of the Additive Group 2.Hilbert's Satz 90 3.The Brauer Group 4.The Milnor K—Groups 5.Dimension of Fields Chapter Ⅶ:Cohomology of Local Fields 1.Cohomology of the Multiplicative Group 2.The ...
6.4 Permutations and Symmetric Polynomials 6.5 The Fundamental Theorem of Algebra: Proof Three 6.6 An Application——The Transcendence of e and ~r 6.7 The Fundamental Theorem of Symmetric Polynomials Exercises 7 Galois Theory 7.1 Galois Theory Overview 7.2 Some Results From Finite Group Theory...
2. Different and Discriminant 3. Riemann-Roch 4. Metrized o-Modules 5. Grothendieck Groups 6. The Chern Character 7. Grothendieck-Riemann-Roch 8. The Euler-Minkow.ski Characteristic Chapter Ⅳ:Abstract Class Field Theory 1. Infinite Galois Theory 2. Projective and Inductive Limits 3....
7 Inner Product and Bilinear form 8 Spectral Theory Chapter Ⅴ Polynomials in One Variable and Field Theory 1 Algebraically Closed Field 2 Algebraic Extension 3 Algebraic Closure 4 Characteristic and Finite Field 5 Separable Algebraic Extension 6 Galois Theory 7 Solve Equation by Radicals 8 Field ...
Chapter 30 Ruler and Compass Constructible Points and Numbers. Impossible Constructions.Constructible Angles and Polygons.Chapter 31 Galois Theory: Preamble Multiple Roots. Root Field. Extension of a Field. Isomorphism.Roots of Unity. Separable Polynomials. Normal Extensions.Chapter 32 Galois Theory: The...
K/k的Galois群與A(m)/H(m)同構,特別是,類域都是相對Abel域。分解定理 對於類域K/k,與前導子f互素的k的素理想p,如f為最小正整數使p𝘧屬於H(f),則在K/k中,可分解為 前導子分歧定理 f由K/k中的分歧素除子構成,且包括所有的分歧素除子。設 ,則f𝗉與範數剩餘的p前導子是一致的,c的...
The Main Conjecture and Annihilation of Class Groups CHAPTER 16 Miscellany Appendix 1. Inverse limits 2. Infinite Galois theory and ramification theory 3. Class field theory Tables 1. Bernoulli numbers 2. Irregular primes 3. Relative class numbers 4. Real class numbers Bibliography List of Symbols ...
16.3. The non-p-part of the class number in a Zp-extension Appendix 1. Inverse limits 2. Infinite Galois theory and ramification theory 3. Class field theory Tables 1. Bernoulli numbers 2. Irregular primes 3. Relative class numbers 4. Real class numbers Bibliography List of Symbols Index ...
3. The Main Theorems of Class Field Theory 4. The Idelic Theory 1. Places of a Number Field 2. A Little Topology 3. The Group of Id^ies of a Number Field 4. Cohomology of Finite Cyclic Groups and the Herbrand Quotient 5. Cyclic Galois Action on Ideles 5. Artin Reciprocity 1. The ...
2.1.7.7 Galois rings 2.1.8 Finite field related books 2.1.8.1 Textbooks 2.1.8.2 Finite field theory 2.1.8.3 Applications 2.1.8.4 Algorithms 2.1.8.5 Conference proceedings 2.2 Tab
5.3 string theory and number theory 5.4 rational curves on algebraic k3 surfaces 6 rigidity 6.1 yau's conjecture about rigidity of some complex manifolds 6.2 geometric proof of margulis' superrigidity 6.3 geometric proof of kazhdan theorem about galois conjugation of shimura varieties references...
4Ellipticcurvesoverarationalfunctionfieldandgeneralizations 5Concludingremarks References Lecturesonp-adicZetaFunctionsand(ч,г)-modules 1Introduction 2Continuousfunctions,measuresanddistributionsoverZp 3Thep-adiczetafunctionofKubota-Leopoldt 4(ч,г)-modulesandGaloiscohomology 5(ч,г)-modulesandIwasawatheory ...
6.2.6 Points,T—valued Points and Geometric Points Closed Points and Geometric Points on varieties 6.2.7 Flat Morphisms The Concept of Flatness Representability of functors 6.2.8 Theory of descend Effectiveness for affine descend data 6.2.9 Galois descend A geometric interpretation Descend for...
6.2.6 Points,T—valued Points and Geometric Points Closed Points and Geometric Points on varieties 6.2.7 Flat Morphisms The Concept of Flatness Representability of functors 6.2.8 Theory of descend Effectiveness for affine descend data 6.2.9 Galois descend A geometric interpretation Descend for...
