THE THEORY OF ALGEBRAIC NUMBERSpdf电子书版本下载

点此进入-本书在线PDF格式电子书下载【推荐-云解压-方便快捷】直接下载PDF格式图书。移动端-PC端通用
下载压缩包 [复制下载地址] 温馨提示：（请使用BT下载软件FDM进行下载）软件下载地址页

THE THEORY OF ALGEBRAIC NUMBERSPDF格式电子书版下载

下载的文件为RAR压缩包。需要使用解压软件进行解压得到PDF格式图书。

建议使用BT下载工具Free Download Manager进行下载,简称FDM(免费,没有广告,支持多平台）。本站资源全部打包为BT种子。所以需要使用专业的BT下载软件进行下载。如 BitComet qBittorrent uTorrent等BT下载工具。迅雷目前由于本站不是热门资源。不推荐使用！后期资源热门了。安装了迅雷也可以迅雷进行下载！

（文件页数 要大于 标注页数，上中下等多册电子书除外）

注意：本站所有压缩包均有解压码： 点击下载压缩包解压工具

CHAPTER Ⅰ．Divisibility 1

1．The uniqueness of factorization 1

2．A general problem 5

3．The Gaussian integers 7

CHAPTER Ⅱ．The Gaussian Primes 12

1．Rational and Gaussian primes 12

2．Congruences 12

3．Determination of the Gaussian primes 16

4．Fermat＇s theorem for Gaussian primes 19

CHAPTER Ⅲ．Polynomials over a field 22

1．Divisibility properties of polynomials 22

2．The Eisenstein irreducibility criterion 26

3．Symmetric polynomials 31

CHAPTER Ⅳ．Algebraic Number Fields 35

1．Numbers algebraic over a field 35

2．Extensions of a field 37

3．Algebraic and transcendental numbers 42

CHAPTER Ⅴ．Bases 47

1．Bases and finite extensions 47

2．Properties of finite extensions 50

3．Conjugates and discriminants 52

4．The cyclotomic field 55

CHAPTER Ⅵ．Algebraic Integers and Integral Bases 58

1．Algebraic integers 58

2．The integers in a quadratic field 61

3．Integral bases 63

4．Examples of integral bases 66

CHAPTER Ⅶ．Arithmetic in Algebraic Number Fields 71

1．Units and primes 71

2．Units in a quadratic field 73

3．The uniqueness of factorization 76

4．Ideals in an algebraic number field 78

CHAPTER Ⅷ．The Fundamental Theorem of Ideal Theory 82

1．Basic properties of ideals 82

2．The classical proof of the unique factorization theorem 86

3．The modern proof 92

CHAPTER Ⅸ．Consequences of the Fundamental Theorem 96

1．The highest common factor of two ideals 96

2．Unique factorization of integers 98

3．The problem of ramification 101

4．Congruences and norms 103

5．Further properties of norms 107

CHAPTER Ⅹ．Class-Numbers and Fermat＇s Problem 111

1．Class numbers 111

2．The Fermat conjecture 115

CHAPTER ⅩⅠ．Minkowski＇s Lemma and the Theory of Units 125

1．The Minkowski lemma 125

2．Applications 131

3．The Dirichlet-Minkowski theorem on units 132

4．The existence of r independent units 134

5．The second part of the proof 137

6．The proof completed 140

References 142

Index 143