抽像代数基础教程英文版第2版PDF电子书下载

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Chapter 1 Number Theory 1

1.1．Induction 1

1.2．Binomial Coefficients 17

1.3．Greatest Common Divisors 36

1.4．The Fundamental Theorem of Arithmetic 58

1.5．Congruences 62

1.6．Dates and Days 73

Chapter 2 Groups Ⅰ 82

2.1．Functions 82

2.2．Permutations 97

2.3．Groups 115

Symmetry 128

2.4．Lagrange's Theorem 134

2.5．Homomorphisms 143

2.6．Quotient Groups 156

2.7．Group Actions 178

2.8．Counting with Groups 194

Chapter 3 Commutative Rings Ⅰ 203

3.1．First Properties 203

3.2．Fields 216

3.3．Polynomials 225

3.4．Homomorphisms 233

3.5．Greatest Common Divisors 239

Euclidean Rings 252

3.6．Unique Factorization 261

3.7．Irreducibility 267

3.8．Quotient Rings and Finite Fields 278

3.9．Officers,Fertilizer,and a Line at Infinity 289

Chapter 4 Goodies 301

4.1．Linear Algebra 301

Vector Spaces 301

Linear Transformations 318

Applications to Fields 329

4.2．Euclidean Constructions 332

4.3．Classical Formulas 345

4.4．Insolvability of the General Quintic 363

Formulas and Solvability by Radicals 368

Translation into Group Theory 371

4.5．Epilog 381

Chapter 5 Groups Ⅱ 385

5.1．Finite Abelian Groups 385

5.2．The Sylow Theorems 397

5.3．The Jordan-H？1der Theorem 408

5.4．Presentations 420

Chapter 6 Commutative Rings Ⅱ 437

6.1．Prime Ideals and Maximal Ideals 437

6.2．Unique Factorization 445

6.3．Noetherian Rings 456

6.4．Varieties 462

6.5．Gr？bner Bases 480

Generalized Division Algorithm 482

Gr？bner Bases 493

Hints to Exercises 505

Bibliography 519

Index 521

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