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基础代数 英文PDF|Epub|txt|kindle电子书版本网盘下载
- （英）卡恩著 著
- 出版社： 北京：世界图书北京出版公司
- ISBN：9787510094644
- 出版时间：2015
- 标注页数：465页
- 文件大小：69MB
- 文件页数：476页
- 主题词：代数－英文
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图书目录
1．Sets1
1.1 Finite,Countable and Uncountable Sets1
1.2 Zorn's Lemma and Well-ordered Sets8
1.3 Graphs15
2．Groups25
2.1 Definition and Basic Properties25
2.2 Permutation Groups32
2.3 The Isomorphism Theorems34
2.4 Soluble and Nilpotent Groups37
2.5 Commutators42
2.6 The Frattini Subgroup and the Fitting Subgroup46
3．Lattices and Categories51
3.1 Definitions;Modular and Distributive Lattices51
3.2 Chain Conditions60
3.3 Categories65
3.4 Boolean Algebras70
4．Rings and Modules79
4.1 The Definitions Recalled79
4.2 The Category of Modules over a Ring84
4.3 Semisimple Modules91
4.4 Matrix Rings96
4.5 Direct Products of Rings101
4.6 Free Modules105
4.7 Projective and Injective Modules110
4.8 The Tensor Product of Modules117
4.9 Duality of Finite Abelian Groups125
5．Algebras131
5.1 Algebras;Definition and Examples131
5.2 The Wedderburn Structure Theorems137
5.3 The Radical141
5.4 The Tensor Product of Algebras146
5.5 The Regular Representation;Norm and Trace153
5.6 M？bius Functions157
6．Multilinear Algebra165
6.1 Graded Algebras165
6.2 Free Algebras and Tensor Algebras168
6.3 The Hilbert Series of a Graded Ring or Module173
6.4 The Exterior Algebra on a Module179
7．Field Theory189
7.1 Fields and their Extensions189
7.2 Splitting Fields195
7.3 The Algebraic Closure of a Field200
7.4 Separability203
7.5 Automorphisms of Field Extensions206
7.6 The Fundamental Theorem of Galois Theory211
7.7 Roots of Unity217
7.8 Finite Fields223
7.9 Primitive Elements;Norm and Trace227
7.10 Galois Theory of Equations232
7.11 The Solution of Equations by Radicals238
8．Quadratic Forms and Ordered Fields249
8.1 Inner Product Spaces249
8.2 Orthogonal Sums and Diagonalization252
8.3 The Orthogonal Group of a Space256
8.4 The Clifford Algebra and the Spinor Norm259
8.5 Witt's Cancelation Theorem and the Witt Group of a Field268
8.6 Ordered Fields272
8.7 The Field of Real Numbers275
8.8 Formally Real Fields279
8.9 The Witt Ring of a Field291
8.10 The Symplectic Group298
8.11 Quadratic Forms in Characteristic Two301
9．Valuation Theory307
9.1 Divisibility and Valuations307
9.2 Absolute Values312
9.3 The p-adic Numbers322
9.4 Integral Elements331
9.5 Extension of Valuations336
10．Commutative Rings347
10.1 Operations on Ideals347
10.2 Prime Ideals and Factorization349
10.3 Localization354
10.4 Noetherian Rings361
10.5 Dedekind Domains362
10.6 Modules over Dedekind Domains371
10.7 Algebraic Equations376
10.8 The Primary Decomposition380
10.9 Dimension386
10.10 The Hilbert Nullstellensatz391
11．Infinite Field Extensions397
11.1 Abstract Dependence Relations397
11.2 Algebraic Dependence402
11.3 Simple Transcendental Extensions405
11.4 Separable and p-radical Extensions409
11.5 Derivations414
11.6 Linearly Disjoint Extensions418
11.7 Composites of Fields427
11.8 Infinite Algebraic Extensions431
11.9 Galois Descent437
11.10 Kummer Extensions441
Bibliography449
List of Notations453
Author Index457
Subject Index459